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): | 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. |
1. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k}\) |
2. | \(18 \hat{i}+13 \hat{j}-2 \hat{k}\) |
3. | \(6 \hat{i}+2 \hat{j}-3 \hat{k}\) |
4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
A string is wrapped along the rim of a wheel of 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 \(2\) seconds is:
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s