A particle is released from a height $H$. At a certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are
$\frac{H}{3},\sqrt {\frac{{2gH}}{3}} $
$\frac{H}{3},2\sqrt {\frac{{gH}}{3}} $
$\frac{{2H}}{3},\sqrt {\frac{{2gH}}{3}} $
$\frac{H}{3},\sqrt {2gH} $
$A$ block of mass $m$ slides down a plane inclined at an angle $\theta$ . Which of the following will $NOT$ increase the energy lost by the block due to friction?
The graph between the resistive force $ F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25\, kg$ and initial velocity is $2\, m/s$. When the distance covered by the body is $4m$, its kinetic energy would be .............. $\mathrm{J}$
A spherical ball of mass $20\, kg$ is stationary at the top of a hill of height $100 \,m$. It slides down a smooth surface to the ground, then climbs up another hill of height $30 \,m$ and finally slides down to a horizontal base at a height of $20 \,m$ above the ground. The velocity attained by the ball is ............... $\mathrm{m} / \mathrm{s}$
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 bullet looses ${\left( {\frac{1}{n}} \right)^{th}}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be