Exercise (Conceptual Questions)

A $2 \mathrm{kg}$ mass lying on a table is displaced in the horizontal direction through $50$ $\mathrm{cm}.$ The work done by the normal reaction will be

A force $\overrightarrow{F}=\left(5\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right) \mathrm{N}$ acts on a body and produces a displacement $\overrightarrow{s}=\left(6\hat{\mathrm{i}}-5\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right) \mathrm{m}$. The work done will be

A force acts on a $3 \mathrm{gm}$ particle in such a way that the position of the particle as a function of time is given by $x=3t-4t^2+t^3,$ where $x$ is meters and $t$ is in seconds. The work done during the first $4$ second is

The kinetic energy of a body becomes four times its initial value. The new momentum will be.

A body of mass $m$ starting from rest from origin moves along $x$ -axis with constant power $\left(P\right).$ Calculate relation between velocity/distance.

A body of mass $4 \mathrm{kg}$ is moving up an inclined plane rising $1$ in $40$ with velocity $40 \mathrm{m} {\mathrm{s}}^{-1}$. If efficiency is $50\%$ then calculate the power required.

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30°$ and $60°$ from vertical (lowest position) are $T_1$ and $T_2$ respectively then

The potential energy of spring when stretched by a distance $x$ is $E.$ The energy of the spring when stretched by $x/2$ is -