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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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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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
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If a person standing on a rotating disc stretches out his hands, the angular speed will

1.  increase

2.  decrease

3.  remain same

4.  None of these

Concept Questions :-

Angular momentum
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If the earth were to suddenly contract to $\frac{1}{n}$th of its present size without any change in its mass, the duration of the new day will be nearly

1.  24/n hours

2.  24 n hours

3.  24/${\mathrm{n}}^{2}$ hours

4.   24 ${\mathrm{n}}^{2}$ hours

Concept Questions :-

Angular momentum
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A constant torque of 31.4 N-m is exerted on a pivoted wheel. If angular acceleration of wheel is , then the moment of inertia of the wheel is

(1) 2.5 $kg-{m}^{2}$

(2)

(3)

(4)

Concept Questions :-

Torque
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The moment of inertia of a flywheel having kinetic energy 360 J and angular speed of 20 rad/s is

1.  18 kg${\mathrm{m}}^{2}$

2.   1.8 kg${\mathrm{m}}^{2}$

3.   2.5 kg${\mathrm{m}}^{2}$

4.   9 kg${\mathrm{m}}^{2}$

Concept Questions :-

Angular momentum