Embibe Experts Solutions for Chapter: Laws of Motion & Work, Energy and Power, Exercise 1: VITEEE 2017

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

A particle covers half of the circle of radius $r$. Then the displacement and distance of the particle are respectively

A particle having a mass $0.5 \mathrm{kg}$ is projected under gravity with a speed of $98 \mathrm{m} {\sec }^{-1}$ at an angle of $60°$.  The magnitude of the change in momentum (in $\mathrm{N} \sec$) of the particle after $10 \mathrm{seconds}$ is $\left[g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right]$

A man holding a rifle (mass of person and rifle together is $100 \mathrm{kg}$) stands on a smooth surface and fires $10$ shots horizontally in $5 \sec$. Each bullet has a mass $10 \mathrm{g}$ with a muzzle velocity of $800 \mathrm{m} {\mathrm{s}}^{-1}.$ The velocity which the rifle man attains after firing $10$ shots will be

Escape velocity when a body of mass $m$ is thrown vertically from the surface of the earth is $v\text{,}$ what will be the escape velocity of another body of mass $4 \mathrm{m}$ is thrown vertically

A solid cylinder of mass $m$ and radius $R$ rolls down inclined plane without slipping. The speed of its $C.M.$ when it reaches the bottom is___

A $5000 \mathrm{kg}$ rocket is set for vertical firing. The exhaust speed is  $800\hspace{0.17em}\mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}$.  To give an initial upward acceleration of $20 \mathrm{m} {\mathrm{s}}^{-2}$, the amount of gas ejected per second to supply the needed thrust will be:  $\left(\mathrm{g}=10\mathrm{\hspace{0.17em}}\mathrm{m}\mathrm{\hspace{0.17em}}{\mathrm{s}}^{-2}\right)$

A block of mass $5 \mathrm{kg}$ resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5 \mathrm{kg}$. The coefficient of kinetic friction between the block and the surface is $0.5$. Tension in the cord is $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$