An elevator is descending  with uniform acceleration. If the force exerted by the block $A$ on the block $B$ is $4 \mathrm{N}$, what is the acceleration of the lift, if the mass of the block $A$ is $\frac{1}{2} \mathrm{kg}$?

The sum of the three vectors in the figure below is zero. The magnitude of $\overrightarrow{\mathrm{OC}}$ and $\overrightarrow{\mathrm{OB}}$ is,

The block $Q$ is pulled on a straight horizontal surface making an angle $\mathrm{\theta }$ with the horizontal. If $a$ is the acceleration of the block, $N$ the contact force by the surface, $T$ the pull of the string along with it and $M$ the mass of the block, then

Two forces of magnitudes $4 \mathrm{N}$ and $8 \mathrm{N}$ are acting on a box when the box moves rightward across frictionless horizontal support. The speed of the box at time $t$ is $1{ \mathrm{m} \mathrm{s}}^{-1}$. The change in kinetic energy of the box is

A bullet of mass $20 \mathrm{g}$ moving with a speed of $100 \mathrm{m} {\mathrm{s}}^{-1}$ enters a heavy wooden block and stops after a distance of $50 \mathrm{cm}$. The average resistive force exerted by the block on the bullet is

Two wooden blocks are moving on a smooth horizontal surface such that the block having mass $m$ remains stationary with respect to block of mass $M$ as shown in the figure below. The magnitude of the applied force $P$ is,