One of the combinations from the fundamental physical constants is \({{hc}\over{G}},\) The unit of this expression is

(a)

Kg²

(b)

m³

(c)

S^-1

(d)

m

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

(a)

4%

(b)

5%

(c)

6%

(d)

7%

Which of the following has the highest number of significant figures?

(a)

0.007 m²

(b)

2.64\(\times\)10²⁴kg

(c)

0.0006032 m²

(d)

6.3200 J

If \(\pi=3.14,\) then the value of \({\pi}^{2}\) is

(a)

9.8596

(b)

9.860

(c)

9.86

(d)

9.9

Which of the following pairs of physical quantities have same dimension?

(a)

force and power

(b)

torque and energy

(c)

torque and power

(d)

force and torque

The dimensional formula of Planck's constant h is

(a)

[ML²T^-1]

(b)

[ML²T³]

(c)

[MLT^-1]

(d)

[ML³T^-3]

The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

(a)

[L]

(b)

[LT^-1]

(c)

[LT^-2]

(d)

[LT^-3]

The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

[M^-1L^-3T^-2]

(d)

[ML^-3T²]

If the force is proportional to square of velocity, then the dimension of proportionality constant is

(a)

[MLT⁰]

(b)

[MLT^-1]

(c)

[MLT^-2T]

(d)

[MLT^-1T⁰]

The dimension of \({\left( {\mu}_{0}{\epsilon}_{0} \right)}^{{{1}\over{2}}}\) is

(a)

length

(b)

time

(c)

velocity

(d)

force

The number of significant figures in 2.64\(\times\)10⁴ kg is ______________.

(a)

2

(b)

4

(c)

5

(d)

3

The displacement of a particle moving along x-axis with respect to times is given by x = at + bt²-ct³. The dimensions of b are ______________.

(a)

L^oT^-3

(b)

L^oT^-3

(c)

LT^-2

(d)

LT^-3

The prefix of 10^-18 is ______________.

(a)

femto

(b)

nano

(c)

giga

(d)

atto

Length can't be measured by _____________.

(a)

fermi

(b)

micron

(c)

debye

(d)

light year

Identify the pair of physical quantities having the same dimensions.

(a)

Light year and period of a pendulum

(b)

Angular momentum and torque

(c)

Energy and Modulus of elasticity

(d)

Torque and work

The dimensional formula of permeability of free space m₀ is ______________.

(a)

[MLT^-2A^-2]

(b)

[M⁰L¹T]

(c)

[M⁰L²T^-1A²]

(d)

none of these

Dimensional formula of self inductance is _______________.

(a)

[MLT^-2A^-2]

(b)

[ML²T^-1A^-2]

(c)

[ML²T^-2A^-2]

(d)

[ML^-2T^-2A^-1]

The triple point temperature of water is_______

(a)

-273.16 K

(b)

0 K

(c)

273.16 K

(d)

100 K

Number of significant digits in 32005_______________.

(a)

1

(b)

2

(c)

5

(d)

2

Number of significant digits in 2030______________.

(a)

1

(b)

2

(c)

3

(d)

4

Which one of the following Cartesian coordinate systems is not followed in physics?

(a)

(b)

(c)

(d)

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

(a)

(b)

(c)

(d)

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

(a)

(b)

(c)

(d)

If a particle executes uniform circular motion in the xy plane in clock wise direction, then the angular velocity is in

(a)

+y direction

(b)

+z direction

(c)

-z direction

(d)

-x direction

If an object is thrown vertically up with the initial speed u from the ground, then the time taken by the object  to return back to ground is

(a)

\(\frac{u^2}{2g}\)

(b)

\(\frac{u^2}{g}\)

(c)

\(\frac{u}{2g}\)

(d)

\(\frac{2u}{g}\)

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R_60°

(b)

R_30° = 4R_60°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R_60°

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

(a)

g = 20 ms^-2

(b)

g = 25 ms^-2

(c)

g = 15 ms^-2

(d)

g = 30 ms^-2

Which of the following curves does not represent motion in one dimension?

(a)

(b)

(c)

(d)

The position x of a particle with respect to time t along x-axis is given by x = 9t² + t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x direction?

(a)

54m

(b)

81m

(c)

24m

(d)

32m

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is ______________.

(a)

33.3km/h

(b)

20\(\sqrt{2}\) km/h

(c)

25\(\sqrt{2}\)km/h

(d)

35km/h

The dimension of point mass is _____________.

(a)

0

(b)

1

(c)

2

(d)

kg

The first derivative of position vector with respect to time is _____________.

(a)

velocity

(b)

acceleration

(c)

force

(d)

displacement

The slope of velocity-time graph gives _____________.

(a)

velocity

(b)

acceleration

(c)

force

(d)

displacement

In non-uniform circular motion, the resultant acceleration makes an angle with the radius vector is ___________.

(a)

\(\tan^{-1}(\frac{ra_t}{V^2})\)

(b)

\(\tan_{-1}(\frac{a_t}{(\frac{r}{v^2})})\)

(c)

\(\tan^{-1}(\frac{rv^2}{at})\)

(d)

\(\tan^{-1}(\frac{r+at^2}{v^2})\)

A gun fires two bullets with same velocity at 60° and 30° with horizontal. The bullets strike at the same horizontal distance. The ratio of maximum height for the two bullets is in the ratio of _____________.

(a)

1: 2

(b)

3: 1

(c)

2: 1

(d)

1: 3

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

(a)

inertia of direction

(b)

inertia of motion

(c)

inertia of rest

(d)

absence of inertia

A vehicle is moving along the positive x direction, if sudden brake is applied, then

(a)

frictional force acting on the vehicle is along negative x direction

(b)

frictional force acting on the vehicle is along positive x direction

(c)

no frictional force acts on the vehicle

(d)

frictional force acts in downward direction

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

(a)

Gravitational force exerted by Earth on the book

(b)

Gravitational force exerted by the book on Earth

(c)

Normal force exerted by the book on the table

(d)

None of the above

A particle of mass m sliding on the smooth double inclined plane (shown in figure) will experience

(a)

greater acceleration along the path AB

(b)

greater acceleration along the path AC

(c)

same acceleration in both the paths

(d)

no acceleration in both the paths

Force acting on the particle moving with constant speed is

(a)

always zero

(b)

need not be zero

(c)

always non zero

(d)

cannot be concluded

An object of mass m begins to move on the plane inclined at an angle θ. The coefficient of static friction of inclined surface is μ_s. The maximum static friction experienced by the mass is

(a)

mg

(b)

μ_s mg

(c)

μ_s mg sin ፀ

(d)

μ_s mg cos ፀ

When the object is moving at constant velocity on the rough surface

(a)

net force on the object is zero

(b)

no force acts on the object

(c)

only external force acts on the object

(d)

only kinetic friction acts on the object

When an object is at rest on the inclined rough surface ____________.

(a)

static and kinetic frictions acting on the object is zero

(b)

static friction is zero but kinetic friction is not zero

(c)

static friction is not zero and kinetic friction is zero

(d)

static and kinetic frictions are not zero

The centrifugal force appears to exist

(a)

only in inertial frames

(b)

only in rotating frames

(c)

in any accelerated frame

(d)

both in inertial and non-inertial frames

If a person moving from pole to equator, the centrifugal force acting on him

(a)

increases

(b)

decreases

(c)

remains the same

(d)

increases and then decreases

Action and reaction ___________

(a)

act on two different objects

(b)

have opposite direction

(c)

have equal magnitude

(d)

all of these

A spacecraft of mass M moving with velocity v in free space explodes and breaks into two pieces. After the explosion a mass m of the spacecraft is left stationary. The velocity of  other part is _______________.

(a)

\(\frac { mv }{ M-n } \)

(b)

\(\frac { M+n }{ Mv } \)

(c)

\(\frac { Mv }{ M-m } \)

(d)

\(\frac { Mv }{ m } \)

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge: The force exerted by the wedge on the block will be ____________ (g is acceleration due to gravity)

(a)

mg cosθ

(b)

mg sinθ

(c)

mg

(d)

mg/cosθ

Inertia means ______________.

(a)

inability

(b)

resistance to change its state

(c)

movement

(d)

inertial frame

When a bus starts to move from rest, the passengers experience a sudden backward push is an example for ____________.

(a)

Inertia of motion

(b)

Inertia of direction

(c)

Inertia of rest

(d)

back pull

If the brake is applied in the moving bus suddenly, passengers move forward is an example for _______________.

(a)

Inertia of motion

(b)

Inertia of direction

(c)

Inertia of rest

(d)

back pull

If a car and a scooter have the same momentum, then which one is having greater speed?

(a)

scooter

(b)

car

(c)

both have same velocity

(d)

data insufficient

If the lines of forces act in the same plane, they can be ___________.

(a)

concurrent forces

(b)

coplanar forces

(c)

either concurrent force or coplanar forces

(d)

Lami's force

Which of the following pairs of materials has minimum amount of coefficient of static friction is ___________.

(a)

Glass and glass

(b)

wood and wood

(c)

ice and ice

(d)

steel and steel

Centrifugal force is a _____________.

(a)

pseudo force

(b)

real force

(c)

forced acting towards centre

(d)

none of the above

A uniform force of (2\(\hat { i }\)+\(\hat { j }\)) N acts on a particle of mass 1 kg. The particle displaces from position (3\(\hat { j }\)+\(\hat { k }\)) m to (5\(\hat { i }\)+3\(\hat { j }\)) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

(a)

\(\sqrt2:1\)

(b)

\(1:\sqrt2\)

(c)

2:1

(d)

1:2

A body of mass 1 kg is thrown upwards with a velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms^-2)

(a)

20 J

(b)

30 J

(c)

40 J

(d)

10 J

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

(a)

\(\sqrt{2gR}\)

(b)

\(\sqrt{3gR}\)

(c)

\(\sqrt{5gR}\)

(d)

\(\sqrt{gR}\)

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U(x) versus x will be (where U, is the potential , energy function)

(a)

(b)

(c)

(d)

A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ax³. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential, energy U(x) of the particles

(a)

(b)

(c)

(d)

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

3k

(d)

6k

A particles moves along x-axis from x = 0 to x = 7m under the influence of a force given by f(x) = 12-2x+3x² then the workdone is__________________

(a)

205 J

(b)

390 J

(c)

378 J

(d)

291 J

A ball moves on a frictionless inclined table without slipping. The work done by the table surface on the ball is ____________.

(a)

positive

(b)

negative

(c)

zero

(d)

none

A force\(\overrightarrow { F } =3\hat { i } +c\hat { j } +2\hat { k } \) acting on a particle causes a displacement \(\overrightarrow { S } =(2\hat { i } -3\hat { j } +4\hat { k } )\) in its own direction. If the work done is 8J, then the value of c is ______________.

(a)

0

(b)

6

(c)

2

(d)

1

A body is falling from a height h. After it has fallen a height \(\frac{h}{2}\) it will possess _______________

(a)

only Potential Energy

(b)

only Kinetic Energy

(c)

half potential and half kinetic energy

(d)

more kinetic and less potential energy

When a body falls freely towards the earth, then its T.E. ______________.

(a)

increases

(b)

decreases

(c)

remains constant

(d)

first increases and then decreases

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

If the force and the displacement are at an angle of 180°, then work done is ___________.

(a)

F.S

(b)

-F.S

(c)

0

(d)

F-S

Principle of conservation of linear momentum ______________.

(a)

is applicable when time of impact between 2 colliding particles is extremely small

(b)

when time of impact is moderately small

(c)

when time of impact is large

(d)

is independent of time of impact

Which of the following potential energy curve describes the elastic collision of two billiard balls?(R=radius of each ball)

(a)

(b)

(c)

(d)

A force acts on a 3 g particle, in such a way that the position of the particle as a function of time is given by x = 3t - 4t² + t³, where x is in metres and t is in seconds. The work done during the first 4 second is _____________.

(a)

490 mJ

(b)

450 mJ

(c)

576 mJ

(d)

530 mJ

The unit of power is _______________.

(a)

J

(b)

W

(c)

Js^-1

(d)

both (b) and (c)

A bullet is fired normally on an immovable wooden plank of thickness 2 m. It loses 20% of its kinetic energy in penetrating a thickness 0.2 m of the plank. The distance penetrated by the bullet inside the wooden plank is ____________.

(a)

0.2 m

(b)

0.8 m

(c)

1 m

(d)

1.5 m

The kinetic energy is not conserved in ______________.

(a)

Elastic collision

(b)

Inelastic collision

(c)

both (a) and (b)

(d)

none

The center of mass of a system of particles does not depend upon,

(a)

position of particles

(b)

relative distance between particles

(c)

masses of particles

(d)

force acting on particle

A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

(a)

zero

(b)

 increasing with x

(c)

decreasing with x

(d)

remaining constant

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

(a)

0.25 rad s^-2

(b)

25 rad s^-2

(c)

5 ms^-2 

(d)

25 ms^-2

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

(a)

increases

(b)

decreases

(c)

remains constant

(d)

depends on direction of rotation

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

L

(b)

L/2

(c)

2L

(d)

L/\(\sqrt{2}\)

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

(a)

the center point of the circle

(b)

the point on the circumference of the circle

(c)

any point inside the circle

(d)

any point outside the circle

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

(a)

15MR²/32

(b)

13MR²/32

(c)

11MR²/32

(d)

9MR²/32

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,

(a)

\( \sqrt \frac{4}{3}gh\)

(b)

\( \sqrt \frac{10}{7}gh\)

(c)

\(\sqrt{2gh}\)

(d)

\( \sqrt \frac{1}{2}gh\)

The speed of the center of a wheel rolling on a horizontal surface is v_o.  A point on the rim in level with the center will be moving at a speed of,

(a)

zero

(b)

v_o

(c)

\(\sqrt{2}\)v_o

(d)

2v_o

Two discs of same moment of inertia rotating about their regular axis passing through center and perpendicular to the plane of the disc with angular velocities ω₁ and ω₁. They are brought in to contact face to face coinciding with the axis of rotation. The expression for loss of energy during this process is

(a)

\(\frac{1}{4}\)\(I(\omega _{1}-\omega _{2})^2\)

(b)

\(I(\omega _{ 1 }-\omega _{ 2 })^{ 2 }\)

(c)

\(\frac{1}{8}\)\(I(\omega _{1}-\omega _{2})^2\)

(d)

\(\frac{1}{2}I\)\((\omega _{1}-\omega _{2})^2\)

A round object of mass M and radius R rolls down without slipping along an inclined plane. The fractional force, 

(a)

dissipates kinetic energy as heat

(b)

decreases the rotational motion

(c)

decreases the rotational and transnational motion

(d)

converts transnational energy into rotational energy

Two rings of radius R & nR made from the same wire have the ratio of moments of intertia about an axis passing through their centre equal to 1 : 8. The value of n is

(a)

2

(b)

2\(\sqrt{2}\)

(c)

4

(d)

1/2

M.I. of a ring of mass M and radius R about an axis passing through the centre & perpendicular to the plane is I. What is M.I. about its diameter?

(a)

I

(b)

I/2

(c)

\(I/\sqrt{2}\)

(d)

I + MR²

A point in the system at which whole mass of the body is supposed to be concentrated is called _____________.

(a)

centre of gravity

(b)

centre of mass

(c)

centre of energy

(d)

centre of buoyancy

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

(a)

Moment of inertia

(b)

Angular momentum

(c)

Angular velocity

(d)

Rotational kinetic energy

Which is a vector quantity?

(a)

Angular momentum

(b)

Work

(c)

Potential energy

(d)

Electric energy

Rotational Kinetic energy of a body is ____________.

(a)

\(\frac { 1 }{ 2 } \)mr²

(b)

\(\frac { 1 }{ 2 } \)Iω²

(c)

\(\frac { 1 }{ 2 } \)Iv²

(d)

\(\frac { 1 }{ 2 } \)mω²

While rolling, the path of center of mass of an object is _______________.

(a)

straight line

(b)

parabola

(c)

hyperbola

(d)

circle

In pure rolling, rotational velocity of points at its edges is equal to ____________.

(a)

Rω

(b)

velocity of centre of mass

(c)

translational velocity

(d)

all the above

A solid cylinder of mass 3 kg and radius 10 cm is rotating about its axis with a frequency of 20/\(\pi \). The rotational kinetic energy of the cylinder _____________.

(a)

10\(\pi \)J

(b)

12 J

(c)

\(\frac { 6\times { 10 }^{ 2 } }{ \pi } \)J

(d)

3 J

The torque in rotational motion is analogous to __________ in translational motion

(a)

linear momentum

(b)

mass

(c)

couple

(d)

force

Moment of inertia of a thin uniform rod about an axis passing through the center of mass and perpendicular to the length is _____________.

(a)

\(\frac{1}{3}Ml^{2}\)

(b)

\(\frac{1}{12}Ml^{2}\)

(c)

\(\frac{1}{2}m(l^{2}+b^{2})\)

(d)

ml²