A small steel sphere of mass $m$ is falling vertically through a viscous liquid with a constant speed $v$ . Which row in the table correctly describes the changes with time in the kinetic energy and gravitational potential energy of the sphere?
Kinetic Energy || Gravitational Potential Energy
constant and equal to $\frac{1}{2}\ mv^2$ || decreases at a rate of $mgv$
constant and equal $\frac{1}{2}\ mv^2$ || decreases at a rate of $(mgv\ -½\ mv^2)$
increases at a rate of $mgv$ || decreases at a rate of $mgv$
increases at a rate of $mgv$ || decreases at a rate of ($\frac{1}{2}\ mv^2$ -mgv)
A particle which is experiencing a force, given by $\vec F = 3\vec i -12\vec j$, undergoes a displacement of $\vec d = 4\vec i$ . If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
A force acts on a $2\,kg$ object so that its position is given as a function of time as $x= 3t^2 + 5.$ What is the work done by this force in first $5\,seconds$ ? ................ $\mathrm{J}$
A ball is thrown vertically downwards from a height of $20\, m$ with an initial velocity $v_0$, It collides with the ground, loses $50$ percent of its energy in collision and rebounds same height. The initial velocity $v_0$ .................... $\mathrm{ms}^{-2}$ (Take $g=10 \,ms^{-2}$)
If a shell fired from a cannon, explodes in mid air, then
A ball is released from a height of $10\, m$. If after the impact there is loss of $40\%$ in its energy, the ball shall rise upto- ................. $\mathrm{m}$