Exercise - 1

A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of ball is

A body of mass $4 \mathrm{kg}$ moves under the action of a force $\overrightarrow{F}=\left(4\hat{\mathrm{i}}+12t^2\hat{\mathrm{j}}\right) \mathrm{N}$ where $t$ is the time in second. The initial velocity of the particle is $\left(2\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ If the force is applied for $1 \mathrm{s},$ work done is:

When a spring is stretched by $2 \mathrm{cm}$, it stores $100 \mathrm{J}$ of energy. If it is stretched further by $2 \mathrm{cm}$, the stored energy will be increased by

A body of mass $m$ dropped from a certain height strikes a light vertical fixed spring of stiffness $k\mathit{.}$ The height of its fall before touching the spring if the maximum compression of the spring is equal to $\frac{3mg}{k}$ is:

A particle moves with a velocity $\overrightarrow{v}=(5\hat{\mathrm{i}}-3\hat{\mathrm{j}}+6\hat{\mathrm{k}}) \mathrm{m} {\mathrm{s}}^{-1}$ under the influence of a constant force $\overrightarrow{F}=\left(10\hat{\mathrm{i}}+10\hat{\mathrm{j}}+20\hat{\mathrm{k}}\right) \mathrm{N}$. The instantaneous power applied to the particle is:

The potential energy of a particle in a potential field is $U=\frac{a}{r^2}-\frac{b}{r} \mathrm{J},$ where $a$ and $b$ are positive constants. The value of $r$ in terms of $a$ and $b$ where the  force on the particle is zero. 

A car of mass $m$ starts moving so that its velocity varies according to the law $v=\beta \sqrt{s},$ where $\beta$ is a constant, and $s$ is the distance covered. The total work performed by all the forces which are acting on the car during the first $t$ seconds after the beginning of motion is

An open knife edge of mass $m$ is dropped from a height $h$ on a wooden floor. If the blade penetrates upto the depth $d$ into the wood, the average resistance offered by the wood to the knife edge is