$A$ car is moving on a circular horizontal track of radius $10 \, m$ with a constant speed of $10 \, m/s$. $A$ plumb bob is suspended from the roof of the car by a light rigid rod of length $1.00 \, m$. The angle made by the rod with the vertical is ........ $^o$.

The weight of a man in a stationary lift is $w_1$ and when it is moving downwards with uniform acceleration $a$ is $w_2$. If the ratio $w_1 : w_2 = 4 : 3$,then the value of $a$ is ($g =$ acceleration due to gravity).

$A$ smooth sphere of radius $R$ moves along a straight line with a constant acceleration $a = g$. $A$ particle is placed at the top of the sphere. It is released from there with zero velocity relative to the sphere. What will be its speed relative to the sphere as a function of the angle $\theta$ as the particle slides?

$A$ 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:

$A$ box of mass $m \, kg$ is placed on the rear side of an open truck accelerating at $4 \, m/s^2$. The coefficient of friction between the box and the surface below it is $0.4$. The net acceleration of the box with respect to the truck is zero. The value of $m$ is :- $[g = 10 \, m/s^2]$

$A$ man is standing in a lift which goes up and comes down with the same constant acceleration. If the ratio of the apparent weights in the two cases is $2 : 1$,then the acceleration of the lift is ......... $m/s^2$.