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

Microscopic group of Physics dealt with the study of ____________.

(a)

classical physics

(b)

statistical mechanics

(c)

fluid mechanics

(d)

quantum physics

If momentum ( p ), area ( A ) and time ( T ) are taken to be fundamental quantities, the energy has the dimensional formula 

(a)

[p\({ A }^{ -1 }\)\({ T }^{ 1 }\)]

(b)

[\({ p }^{ 2 }\)\(A^{ 1 }\)\({ T }^{ 1 }\)]

(c)

[\(p^{ 1 }\)\(A^{ -1/2 }\)\({ T }^{ 1 }\)]

(d)

[\(p^{ 1 }\)\(A^{ 1/2 }\)\({ T }^{ -1 }\)]

The significant figures of the number 6.0023 is

(a)

2

(b)

5

(c)

4

(d)

1

The equation of a wave is given by y = a sin \(\omega \left( \frac { x }{ v } -k \right) \) where \(\omega\) is angular velocity and v is the linear velocity. The dimension of k will be

(a)

[T^-2]

(b)

[T^-1]

(c)

[T]

(d)

[LT]

The quantities A and B~are related, by the relation, m = A/B, where m i~.th'J'linear density and A is the force. The dimensions of B are of 

(a)

pressure

(b)

latent heat

(c)

work

(d)

None of these

Sonar emits which of the following waves?

(a)

radio

(b)

light

(c)

microwave

(d)

ultrasound

The pair of quantities having same dimensions is ______________.

(a)

Impulse and Surface Tension

(b)

Angular momentum and Work

(c)

Work and Torque

(d)

Young's modulus and Energy

The maximum possible error in the difference of two quantities is___________.

(a)

Z=A+B

(b)

\(\triangle Z=\triangle A-\triangle B\)

(c)

\(\frac{\triangle Z}{Z}=\frac{\triangle A}{A}+\frac{\triangle B}{B}\)

(d)

\(\frac{\triangle Z}{Z}=\frac{\triangle A\triangle B}{AB}\)

At what angle should the two forces \(2P\) and \(\sqrt { 2 } P\) act,so that the resultant force is \(P\sqrt { 10 } \)?

(a)

\({ 45 }^{ 0 }\)

(b)

\({ 60 }^{ 0 }\)

(c)

\({ 90 }^{ 0 }\)

(d)

\({ 120 }^{ 0 }\)

Given A = \(\hat i \ + \ \hat j \ +\ \hat k\) and B = \(-\hat i \ - \ \hat j \ -\ \hat k\), then (A - B) will make angle with A

(a)

0^o

(b)

180^o

(c)

90^o

(d)

60^o

The connection (a.b)² = a² b² is satisfied when

(a)

a is parallel to b

(b)

a \(\neq \)b

(c)

a.b =1

(d)

a\(\bot \)b

If 2 balls are projected at angles 45° and 60° and the maximum heights reached are same, what is the ratio of their initial velocities ?

(a)

\(\sqrt{2} : \sqrt{3}\)

(b)

\(\sqrt{3} : \sqrt{2}\)

(c)

3 : 2

(d)

2 : 3

A projectile is lauched with a speed of 10 m/s at an angle 60^o with the horizontal from a sloping surface of inclination 30^o. The range R is (Take g = 10 m/s²)

(a)

4.9 m

(b)

13.3 m

(c)

19.1 m

(d)

12.6 m

The velocity vector of the motion described by the position vector of a particle \(r=2t\hat { i } +{ t }^{ 2 }\hat { j } \) is given by

(a)

\(v=2\hat { i } +2t\hat { j } \)

(b)

\(v=2t\hat { i } +2t\hat { j } \)

(c)

\(v=t\hat { i } +{ t }^{ 2 }\hat { j } \)

(d)

\(v=2t\hat { i } +{ t }^{ 2 }\hat { j } \)

Vectors can be added _____________

(a)

algebrically

(b)

geometrically

(c)

graphically

(d)

both (b) and (c)

\(\hat j\times \hat i\) is ____________.

(a)

\(-\hat i\)

(b)

\(-\hat j\)

(c)

\(-\hat k\)

(d)

\(\vec z\)

\(X\propto \frac { 1 }{ Y } \) (or) XY = constant is represented by ___________.

(a)

(b)

(c)

(d)

A block is moving up an inclined plane of inclination 60⁰ with velocity of 20ms^-1 and stops after 2.00 s. if g = 10ms^-1, then the approximate value of coefficient of friction is

(a)

3

(b)

3.3

(c)

0.27

(d)

0.33

An object is moving on a plane surface with uniform velocity 10 ms^-1 in presence of a force 10 N. The frictional force between the object and the surface is

(a)

1 N

(b)

- 10 N

(c)

10 N

(d)

100 N

A mass m rests on a horizontal surface. The coefficient of friction between the mass and the surface is if the mass is pulled by a force F as shown in figure. The limiting friction between mass and the surface will be 

(a)

\(\mu mg\)

(b)

\(\mu[{mg-{({\sqrt3\over2})}}F]\)

(c)

\(\mu[{mg-{({F\over2})}}]\)

(d)

\(\mu[{mg+{({F\over2})}}]\)

A weight w is suspended from the mid-point of a rope, whose ends are at the same level. In order to make the rope perfectly horizontal, the force applied to each of its ends must be

(a)

less than w

(b)

equal to w

(c)

equal to 2w

(d)

infinitely large

A body of mass 40 kg resting on rough horizontal surface is subjected to a force P which is just enough to start the motion of the body \({ \mu }_{ s }\)=0.5, \({ \mu }_{ k }\)=0.4, g=10 ms^-2 and the force P is continuously applied on the body, then the acceleration of the body is

(a)

zero

(b)

1 ms^-2

(c)

2 ms^-2

(d)

2.4 ms^-2

A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle \({ \theta }_{ 1 }\) in the first 2s. In the next 2 s, it rotates through an additional angle \({ \theta }_{ 2 }\), the ratio of \(\frac { { \theta }_{ 2 } }{ { \theta }_{ 1 } } \) is 

(a)

1

(b)

2

(c)

3

(d)

4

Two bodies of mass m and 4m are attached to a spring as shown in the figure. The body of mass m hanging from a string of length I is executing periodic motion with amplitude \(\theta\) = 60^o while other body is at rest on the surface. The minimum coefficient of friction between the mass 4m and the horizontal surface must be

(a)

\(\frac{1}{4}\)

(b)

\(\frac{1}{3}\)

(c)

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

(d)

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

A student whirls a stone in a horizontal circle of radius 3 m and at height 8 m above level ground. The string breaks, at lowest point and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of 20 m. What is the magnitude of the centripetal acceleration of the stone while breaking off.

(a)

150 ms^-2

(b)

140 ms^-2

(c)

81.4 ms^-2

(d)

163  ms^-2

While walking, the vertical component of reactive force balances our ____________.

(a)

force

(b)

mass

(c)

weight

(d)

impulse

The angle friction \(\theta\) is given by ________________.

(a)

tan \(\mu _{ s }\)

(b)

tan^-1 \(\mu _{ s }\)

(c)

\(\frac { { fs }^{ max } }{ N } \)

(d)

sin^-1\(\mu _{ s }\)

For inelastic Collison between two spherical rigid bodies 

(a)

the total kinetic energy is conserved 

(b)

the total mechanical energy is not conserved 

(c)

the linear momentum is not  conserved 

(d)

the linear momentum is conserved

A ballon with mass is descending with an accelration a (where, a<g). How much mass could be removed from it, so that its starts moving up with an accelration a?

(a)

\(\frac { 2ma }{ g+a } \)

(b)

\(\frac { 2ma }{ g-a } \)

(c)

\(\frac { ma }{ g+a } \)

(d)

\(\frac { ma }{ g-a } \)

A body of mass 1 kg moves from points A(2m, 3m, 4m) to B(3m, 2m, 5m). During motion of body, a force \(F=(2N)\hat { i } -(4N)\hat { j } \) acts on it. The work done by the force on the particle during displacement is

(a)

6 J

(b)

2 J

(c)

-2 J

(d)

-6 J

A running man has half the KE that a boy of half his mass has. The man speeds up by 1\({ ms }^{ -1 }\) and then has the same KE as that of boy. The original speeds of man and boy in \({ ms }^{ -1 }\) are

(a)

\(\left( \sqrt { 2 } +1 \right) \),\(\left( \sqrt { 2 } -1 \right) \)

(b)

\(\left( \sqrt { 2 } +1 \right) \),\( 2\left( \sqrt { 2 } +1 \right) \)

(c)

\( \sqrt { 2 } \),\( \sqrt { 2 } \)

(d)

\(\left( \sqrt { 2 } +1 \right) \),\(2\left( \sqrt { 2 } -1 \right) \)

A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction \(\mu \). It is compressed by a distance a from its normal length and, on being released, it moves to a distance b from its equilibrium position. The decrease in amplitude for one half-cycle (-a to b) is

(a)

\(\frac { \mu mg }{ K } \)

(b)

\(\frac { 2\mu mg }{ K } \)

(c)

\(\frac { \mu g }{ K } \)

(d)

\(\frac { K}{ \mu mg } \)

A body of mass 6 kg is acted upon by a force which causes a displacement in it given by \(x=\frac { { t }^{ 2 } }{ 4 } \) metre, where t is the time in second. The work done by the force in 2 s is

(a)

12 J

(b)

9 J

(c)

6 J

(d)

3 J

A plank of mass 10 kg and a block of mass 2 kg are placed on a horizontal plane as shown in the figure. There is no friction between plane and plank. The coefficient of friction between block and plank is 0.5. A force of 60 N is applied on plank horizontally. In first 2 s the work done by friction on the block is

(a)

-100 J

(b)

100 J

(c)

zero

(d)

200 J

The net work done by the tension in the figure when the bigger block of mass M touches the ground is 

(a)

+Mgd

(b)

-(M+m)gd

(c)

-mgd

(d)

zero

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is
​​​​​​​

(a)

21J

(b)

26J

(c)

13J

(d)

18J

A block of mass 20 kg is moving in x-direction with a constant speed of 10 ms^-1. It is subjected to a retarding force F = (- 0.1x) N during its travel from x = 20 m to x = 30 m. Its final kinetic energy will be

(a)

975 J

(b)

450 J

(c)

275 J

(d)

250 J

A force F = (10 + 0.5x) acts on a particle in the x-direction. What would be the work done by this force during a displacement from x = 0 to x = 2m (F is in newtons and x in metre)

(a)

31.5 J

(b)

63 J

(c)

21 J

(d)

42 J

The unit of power is _______________.

(a)

J

(b)

W

(c)

Js^-1

(d)

both (b) and (c)

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)

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

The centre of a wheel rolling on a plane surface moves with a speed V₀ A particle on the rim of the wheel at the same level as the centre will be moving at speed

(a)

zero

(b)

V₀ 

(c)

\(\sqrt { 2 } \) V₀ 

(d)

2 V_n

A particle moving in a circular path has an angular momentum of L If the frequency of rotation is halved then its angular momentum becomes

(a)

\(\frac { L }{ 2 } \)

(b)

L

(c)

\(\frac { L }{ 3 } \)

(d)

\(\frac { L }{ 4 } \)

A bullet of mass m and velocity is fired into a block of mass M and sticks to it The final velocity of the system equals

(a)

\(\frac { M }{ m+M } .v\)

(b)

\(\frac { m }{ m+M } .v\)

(c)

\(\frac { m+M }{ m } .v\)

(d)

None of these

 A bullet of mass m is fired into a block of wood of mass M which hangs on the end of pendulum and gets embedded into it.  When the bullet strikes the wooden block, the pendulum starts to swing with maximum rise R.  Then, the velocity of the bullet is given by

(a)

\({M\over m + M}\sqrt{2gR}\)

(b)

\({ M + m\over m}\sqrt{2gR}\)

(c)

\({M\over m}{\sqrt{2gR}}\)

(d)

None of these

A mass m moves with a velocity v and collides inelastically with another identical mass.After collision the 1st mass moves with velocity \(\frac { v }{ \sqrt { 3 } } \) in a direction perpendicular to the initial direction of motion.Find the speed of the 2nd mass after collision 

(a)

\(\frac { 2 }{ \sqrt { 3 } } v\)

(b)

\(\frac { v }{ \sqrt { 3 } } \)

(c)

\(v\)

(d)

\(\sqrt { 3v } \)

Two particles of mass mA and m_b and their velocities are V_A and v_B respectively collides. After collision they interchanges their velocities, then ratio of

(a)

\(v_A\over v_B\)

(b)

\(v_B\over v_A\)

(c)

\(v_A+v_B\over v_B-v_A\)

(d)

1

A block having mass m collides with an another stationary block having mass 2 m. The lighter block comes to rest after collision. If the velocity of first block is V, then the value of coefficient of restitution will must be

(a)

0.5

(b)

0.4

(c)

0.6

(d)

0.8

A uniform rod AB of length I and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml²/3, the initial angular acceleration of the rod will be ____________.

(a)

\(\frac { mgl }{ 2 } \)

(b)

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

(c)

\(\frac { 3g }{ 2l } \)

(d)

\(\frac { 2g }{ 3l } \)

Moment of inertia of a thin uniform rectangular sheet about an axis passing through the center of mass and perpendicular to the plane of the sheet is _______________.

(a)

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

(b)

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

(c)

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

(d)

Ml²