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]

Which unit is used to measure size of a nucleus?

(a)

Angstrom

(b)

Micron

(c)

Nano

(d)

Fermi

The diameter of the steel ball is measured using a vernier calipers which has divisions of 0.5 cm on its main scale and 10 division of its vernier scale match 9 division on the main scale. Three such measurements for a ball are as follows.

S.No	MS (cm)	VS (divisions)
1	0.5	8
2	0.5	4
3	0.5	6

 If the zero error is - 0.03 em, then mean corrected diameter is__________________ cm.

(a)

0.56

(b)

0.53

(c)

0.59

(d)

0.52

One degree of arc is_______________.

(a)

1''

(b)

60''

(c)

60'

(d)

60^o

If \(\bar A\)and \(\bar B\) are two vectors, \(\bar A.\bar B=\bar A\times\bar B\) then resultant vector is ____________.

(a)

A+B

(b)

A-B

(c)

\(\sqrt {A^2+B^2}\)

(d)

\(\sqrt {A^2+B^2+\sqrt{2}AB}\)

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

(a)

E

(b)

F

(c)

C

(d)

D

A car covers half of its journey with a speed of 10 ms^-1 and the other half by 20 ms^-1 The average speed of car during the total journey is _____________.

(a)

70 ms^-1

(b)

15 ms^-1

(c)

13.33 ms^-1

(d)

7.5 ms^-1

Inertia is that property of a body by virtue of which the body is ____________.

(a)

unable to change by itself the state o frest

(b)

unable to change by itself the state of uniform motion

(c)

unable to change by itself the direction of motion

(d)

unable to change by itself the state of rest and ofunifonn linear motion

Inertia means ______________.

(a)

inability

(b)

resistance to change its state

(c)

movement

(d)

inertial frame

A block of mass 3kg is at rest on a rough inclined plane with angle of inclination 30° with horizontal. If \(\mu\)s = 0.7, then the frictional force is ____________.

(a)

17.82 N

(b)

1.81 N

(c)

3.63 N

(d)

2.1 N

A bullet is fired from a rifle. If the rifle recoils, the kinetic energy of the rifle is ____________.

(a)

greater than that of bullet

(b)

equal to that of bullet

(c)

less than that of bullet

(d)

does not change

When a mass is rotating in a plane about a fixed point its angular momentum is directed along ______________.

(a)

A line perpendicular to the plane of rotation

(b)

 The radius

(c)

 The tangent to the circle

(d)

An angle of 45° to the plane of rotation

A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec, The moment of inertia of the wheel about the ax is of rotation is _____________.

(a)

0.6 kgm²

(b)

0.15 kgm²

(c)

0.8 kgm²

(d)

0.75 kgm²

The centre of mass of a solid cone along the line from the center of the base to the vertex is at _____________.

(a)

\(\frac{1}{2}\)th of its height

(b)

\(\frac{1}{3}\)of its height 

(c)

\(\frac{1}{4}\)of its height 

(d)

\(\frac{1}{5}\)of its height 

A liquid is contained in a vertical tube of semicircular cross section the contact angel is zero. The force of surface tension on the curved part & on the flat part are in ratio ______________.

(a)

1 : 1

(b)

1 : 2

(c)

\(\pi\)  : 2 

(d)

2 : \(\pi\)

The pressure at the bottom of a liquid tank does not depend on ________.

(a)

acceleration due to gravity

(b)

density of the liquid

(c)

height of the liquid

(d)

area of the liquid surface

An ideal gas passes from one equilibrium state (P₁, V₁, T₁, N) to another equilibrium state (2P₁, 3V₁, T₂, N). Then

(a)

T₁ = T₂

(b)

\({ T }_{ 1 }=\frac { { T }_{ 2 } }{ 6 } \)

(c)

T₁ = 6T₂

(d)

T₁ = 3T₂

At a given volume and temperature, the pressure of a gas __________.

(a)

varies inversely as its mass

(b)

varies inversely as the square of its mass

(c)

varies linearly as its mass

(d)

is independent of its mass

There is a change in length when a 33000 N tensile force is applied on a steel rod of area of cross-section 10^-3 m². The change of temperature required to produce the same elongation, if the steel rod is heated, is (modulus of elasticity of steel = 3\(\times\)10¹¹ N/m², coefficient of linear expansion of steel = 1.1\(\times\)10^-5/°C)

(a)

20^oC

(b)

15^oC

(c)

10^oC

(d)

0^oC

Ten moles of an ideal gas at constant temperature 600 K is compressed from 100L to 10 L. The work done in the process is_______.

(a)

4.11\(\times\)10⁴ J

(b)

- 4.11\(\times\)10⁴ J

(c)

11.4\(\times\)10⁴J

(d)

-11.4\(\times\)10⁴ J

Which of the following shows the correct relationship between the pressure and density of an ideal gas at constant temperature?

(a)

(b)

(c)

(d)

Kinetic theory ___________.

(a)

Correctly explains specific heat capacities of many liquid

(b)

Correctly explains specific heat capacities of many gases

(c)

Correctly explains specific heat capacities of many solids

(d)

Correctly explains specific heat capacities of many super cooled liquid

Two bodies A and B whose masses are in the ratio 1:2 are suspended from two separate massless springs of force constants k_A and k_B respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is

(a)

\(\sqrt { \frac { { K }_{ B } }{ { 2 }K_{ A } } } \)

(b)

\(\sqrt { \frac { { K }_{ B } }{ { 8 }K_{ A } } } \)

(c)

\(\sqrt { \frac { {2 K }_{ B } }{ { }K_{ A } } } \)

(d)

\(\sqrt { \frac { {8 K }_{ B } }{ { }K_{ A } } } \)

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

(a)

4\(\frac { Mg }{ k } \)

(b)

\(\frac { Mg }{ k } \)

(c)

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

(d)

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

A particle executing simple harmonic motion has a kinetic energy K_o cos² ωt. The maximum values of the potential energy and the total energy are, respectively ________.

(a)

k₀/2 and k₀

(b)

k₀ and 2k₀

(c)

k₀ and k₀

(d)

0 and 2k₀