The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii in the ratio of \(1:2\) is:
1. \(2:1\)
2. \(4:1\)
3. \(1:2\)
4. \(1:4\)
A string is wrapped along the rim of a wheel of the moment of inertia \(0.10\) kg-m2 and radius \(10\) cm. If the string is now pulled by a force \(10\) N, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2\) s is:
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s
Assertion (A): | For a body under translatory as well as rotational equilibrium, net torque about any axis is zero. |
Reason (R): | \( \Sigma \vec{F}_{i}=0 \text { and } \Sigma\left(\vec{r}_{i} \times \vec{F}_{i}\right)=0 \) implies that \( \Sigma\left(\vec{r}_{i}-\overrightarrow{r_{0}}\right) \times \vec{F}=0 \). | Together
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | The axis of rotation of a rigid body cannot lie outside the body. |
Reason (R): | It must pass through a material particle of the body. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
The ratio of the radius of gyration of a circular disc to that of a circular ring, both having the same mass and radius, about their respective axes is:
1. \(\sqrt2:\sqrt3\)
2. \(\sqrt3:\sqrt2\)
3. \(1:\sqrt2\)
4. \(\sqrt2:1\)