Work, Energy & Power · JEE Main previous year questions

A force $\vec{F}=(5\vec{i}+3\vec{j}+2\vec{k})\mathrm{N}$ is applied over a particle which displaces it from its origin to the point $\vec{r}=(2\vec{i}-\vec{j})\mathrm{m}$. The work done on the particle in joules is

1. A.$+10$
2. B.$+7$
3. C.$-7$
4. D.$+13$

A body of mass ${}^{\prime }{m}^{\prime }$, accelerates uniformly from rest to ${}^{\prime }{v}_1^{\prime }$ in time $T$. The instantaneous power delivered to the body as a function of time is given by

1. A.$\frac{m{v}_1{t}^2}{T}$
2. B.$\frac{m{v}_1^{2}t}{T^2}$
3. C.$\frac{m{v}_{1}t}{T}$
4. D.$\frac{m{v}_1^{2}t}{T}$

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

1. A.$\frac{1}{4}mgR$
2. B.$2mgR$
3. C.$\frac{1}{2}mgR$
4. D.$mgR$

A wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching is

1. A.$2Fl$
2. B.$Fl$
3. C.$\frac{F}{2l}$
4. D.$\frac{Fl}{2}$

A ball whose kinetic energy is E, is projected at an angle of $45^{\circ }$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

1. A.E
2. B.$\frac{E}{\sqrt{2}}$
3. C.$\frac{E}{2}$
4. D.zero

The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$) to infinity is

1. A.$mgR/2$
2. B.$2mgR$
3. C.$mgR$
4. D.$mgR/4$

A spring of force constant $800N/m$ has an extension of $5\mathrm{cm}$. The work done in extending it from $5\mathrm{cm}$ to $15\mathrm{cm}$ is

1. A.$16\mathrm{J}$
2. B.$8\mathrm{J}$
3. C.$32\mathrm{J}$
4. D.$24\mathrm{J}$