A bullet of mass $25\,g$ moving with a velocity of $200\,m/s$ is stopped within $5\,cm$ of the target. The average resistance offered by the target is ............... $\mathrm{kN}$

A bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistances of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $\mathrm{ms}^{-1}$

Which of the following graphs is correct between kinetic energy $ (E), $ potential energy $(U)$  and height $(h)$ from the ground of the particle

A block of mass $2\, kg$ is placed on a rough inclined plane as shown in the figure $(\mu = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The  spring will be compressed to a maximum of .............. $\mathrm{cm}$

A cyclist comes to a skidding stop in $10 \;m$. During this process, the force on the cycle due to the road is $200\; N$ and is directly opposed to the motion.

$(a)$ How much work does the road do on the cycle ?

$(b)$ How much work does the cycle do on the road ?

A body of $\mathrm{m} \mathrm{kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:

(given, $\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\sqrt{2}=1.4$ )