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

A 20 kg solid disc rolls on a horizontal surface at the rate of 4 $m{s}^{-1}$. Its total kinetic energy is 

1.  60 J

2.  120 J

3.  240 J

4.  80 J

The centre of the mass of \(3\) particles, \(10~\text{kg},\)  \(20~\text{kg},\) and \(30~\text{kg},\) is at \((0,0,0).\) Where should a particle with a mass of \(40~\text{kg}\) be placed so that its combined centre of mass is \((3,3,3)?\)
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)

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

A particle performs uniform circular motion with an angular momentum L. If the frequency of the particle motion is double, the angular momentum becomes

1. 2L

2. 4L

3. $\frac{L}{2}$

4. $\frac{L}{4}$

The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:

In figure (a), a meter stick, half of which is wood and the other half steel is pivoted at the wooden end at O and a force F is applied to the steel end a. In figure (b) the stick is pivoted at the steel eid at O' and the same force F is applied at the wooden end at a' The angular acceleration

1.  in (a) is greater than in (b)

2.  in (b) is greater than in (a)

3.  equal both in (a) and (b)

4.  none of the above.

A sqaure lamina is as shown in figure. The moment of inertia of the frame about the three axes shown in figure are $I_1,<mspace\; width="1em"></mspace>I_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>I_3$ respectively. Select the correct alternative.

1. $I_2=I_3>I_1$

2. $I_1>I_2>I_3$

3. $I_2=I_3<I_1$

4. $I_1<I_2<I_3$

                
1. \(\dfrac{7ma^2}{16}\)
2. \(\dfrac{3ma^2}{16}\)
3. \(\dfrac{3ma^2}{4}\)
4. \(\dfrac{9ma^2}{16}\)