If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of

1.  6 hours

2.  12 hours

3.  18 hours

4.  24 hours

Concept Questions :-

Angular momentum
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A wheel has angular acceleration of 3.0 rad/$se{c}^{2}$ and an initial angular speed of 2.00 rad/sec.  In a time of 2 sec it has rotated through an angle (in radian) of

(1) 10                (2) 12

(3) 4                  (4) 6

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The bob A of a simple pendulum is released when the string makes an angle of 450 with the vertical. It hits another bob B of the same material and the same mass kept at rest on a table. If the collision is elastic

1.  Both A and B rise to the same height

2.  Both A and B come to rest at B

3.  Both A and B move with the same velocity of A

4.  A comes to rest and B moves with the velocity of A

Concept Questions :-

Linear momentum
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If a force acts on a body at a point away from the centre of mass, then

1.  Linear acceleration changes

2.  Angular acceleration changes

3.  Both change

4.  None of these

Concept Questions :-

Torque
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If the linear density of a rod of length 3m varies as $\lambda$=2+x, then the position of the center of mass of the rod is at a distance of

1.  $\frac{7}{3}m$

2.  $\frac{10}{7}m$

3.  $\frac{12}{7}m$

4.  $\frac{9}{7}m$

Concept Questions :-

Center of mass
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Difficulty Level:

A sphere cannot roll on

1.  a smooth horizontal surface

2.  a rough horizontal surface

3.  a smooth inclined surface

4.  a rough inclined surface

Concept Questions :-

Rolling motion
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Two balls are thrown simultaneously in the air. The acceleration of the center of mass of the two balls while in air

1.  depends on the direction of the motion of the balls

2.  depends on the masses of the two balls

3.  depends on the speeds of two balls

4.  is equal to g

Concept Questions :-

Center of mass
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A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizotal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

(1) $\sqrt{\frac{2gh}{I+mr}}$

(2) $\sqrt{\frac{2mgh}{I+m{r}^{2}}}$

(3) ${\left[\frac{2mgh}{I+2m}\right]}^{\frac{1}{2}}$

(4) $\sqrt{2gh}$

Concept Questions :-

Rolling motion
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If a body of mass m collides head on, elastically with velocity u with another identical body at rest. After collision velocity of the second body will be

(1) zero

(2) u

(3) 2u

(4) data insufficient

Concept Questions :-

Center of mass
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Difficulty Level:

A particle of mass m at rest is acted upon by a constant force F for a time t. Its kinetic energy after an interval t is

1.  $\frac{{\mathrm{F}}^{2}{\mathrm{t}}^{2}}{\mathrm{m}}$

2.  $\frac{{\mathrm{F}}^{2}{\mathrm{t}}^{2}}{2\mathrm{m}}$

3.  $\frac{{\mathrm{F}}^{2}{\mathrm{t}}^{2}}{3\mathrm{m}}$

4.  $\frac{\mathrm{Ft}}{2\mathrm{m}}$

Concept Questions :-

Linear momentum