$A$ block of mass $M$ placed inside a box descends vertically with acceleration $a$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of $a$ will be .............

$A$ vehicle is moving with a constant speed of $10 \ m/s$ on a circular horizontal track of radius $20 \ m$. $A$ bob is suspended from the roof of the vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity,$g = 10 \ m/s^2$).

$A$ body of mass $1.0 \, kg$ is falling with an acceleration of $10 \, m/s^2$. Its apparent weight will be ......... $kg \, wt$ $(g = 10 \, m/s^2)$.

$A$ solid sphere of mass $2\, kg$ is resting inside a cube as shown in the figure. The cube is moving with a velocity $\vec v = (5t\,\hat i + 2t\,\hat j)\,m/s$. Here $t$ is the time in seconds. All surfaces are smooth. The sphere is at rest with respect to the cube. Find the total force $N$ exerted by the sphere on the cube. (Take $g = 10\, m/s^2$)

$A$ coin is dropped in a lift. It takes time $t_1$ to reach the floor when the lift is stationary. It takes time $t_2$ when the lift is moving up with constant acceleration. Then:

The mass of a person sitting in a lift is $50 \, kg$. If the lift is coming down with a constant acceleration of $10 \, m/s^2$,then the reading of the spring balance will be ......... $N$ $(g = 10 \, m/s^2)$.