Work Power and Energy

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below

A bullet is fired into a fixed target looses one third of its velocity after travelling $4 \mathrm{~cm}$. It penetrates further $\mathrm{D} \times 10^{-3} \mathrm{~m}$ before coming to rest. The value of $\mathrm{D}$ is :

The potential energy function (in $J$ ) of a particle in a region of space is given as $U=\left(2 x^2+3 y^3+2 z\right)$. Here $x, y$ and $z$ are in meter. The magnitude of $x$-component of force (in $N$ ) acting on the particle at point $P(1,2,3) \mathrm{m}$ is :

A body of mass $2 \mathrm{~kg}$ begins to move under the action of a time dependent force given by $\vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N$. The power developed by the force at the time $t$ is given by:

If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

A bullet of mass $50 \mathrm{~g}$ is fired with a speed $100 \mathrm{~m} / \mathrm{s}$ on a plywood and emerges with $40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$, have same momentum, respectively. The particle with maximum kinetic energy is :