JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Work, Power & Energy

Given below are two statements:
Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-{\int }_{r_1}^{r_2}\vec{F}\cdot \overrightarrow{dr}$.
Statement II: Any object moving from one l …

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch e …

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $\mathrm{x}(\mathrm{t})=\alpha {\mathrm{t}}^2+\beta \mathrm{t}+\gamma \mathrm{m}$, where $\alpha =1\mathrm{m}/{\mathrm{s}}^2$, $\beta =1\mathrm{m}/\mathrm{s}$ an …

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is $\_\_\_\_$ N.

A 1 kg block subjected to two simultaneous forces $(2\hat{i}+3\hat{j}+4\hat{k})$ N and $(3\hat{i}-\hat{j}-2\hat{k})$ N is moved a distance of 25 m along $(3\hat{i}-4\hat{j})$ direction. The work done in this process is _____ J.