Write the similarity between various forms of energy.

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A particle is projected vertically upwards with a speed of $16\  m/s$ , after some time , when it again passes through the point of projection, its speed is found to be $8\  m/s$ . It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is ...................... $\mathrm{m}$ ( $g$ = $10\  m/s^2$ )

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 $g=10 \,ms^{-2}$)

  • [AIPMT 2015]

A body of mass $8\,kg$ is moved by a force $F = 3x\,N,$ where $x$ is the distance covered. Initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s.$ The final speed is  ........... $m/s$

A particle experiences a variable force $\overrightarrow{ F }=\left(4 x \hat{ i }+3 y ^{2} \hat{ j }\right)$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $x-y$ plane, the Kinetic Energy changes by............$j$

  • [JEE MAIN 2022]

A boy is rolling a $0.5\, kg$ ball on the frictionless floor with the speed of $20\, ms ^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5 \%$ of its initial kinetic energy. What is the speed of the ball now ? (in $ms ^{-1}$)

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