$A$ block of mass $m$ is resting on a wedge of angle $\theta$ as shown in the figure. The wedge is given a horizontal acceleration $a$. What is the minimum value of $a$ so that the mass $m$ falls freely?

An object of mass $2 \, kg$ is placed at rest in a frame $S_1$ moving with velocity $10 \hat{i} + 5 \hat{j} \, m/s$ and having acceleration $5 \hat{i} + 10 \hat{j} \, m/s^2$. The object is also seen by an observer standing in a frame $S_2$ moving with velocity $5 \hat{i} + 10 \hat{j} \, m/s$. Calculate the pseudo force acting on the object. Which frame is responsible for this force?

$A$ metallic rod of length $L$ and mass $M$ is moving under the action of two unequal forces $F_1$ and $F_2$ (directed opposite to each other) acting at its ends along its length. Ignore gravity and any external magnetic field. If the specific charge of electrons is $(e/m)$,then the potential difference between the ends of the rod in steady state must be:

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

The readings shown in two extended spring balances,$S_1$ and $S_2$,are $60\,kg$ and $30\,kg$ respectively. The lift is accelerating upward with an acceleration of $10\,m/s^2$. The mass $m$ is stationary with respect to the lift. Then the mass of the block will be ......... $kg$. (Take $g = 10\,m/s^2$)

$A$ truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of $a$. The pendulum will tilt: