Work, Energy & Power · JEE Main previous year questions

2012 2 questions

1. Q352012 · 12 May 2012 · Shift 1

   Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be

   1. A.$m\frac{v_0^2}{x_0^2}$
   2. B.$m\frac{v_0}{2x_0}$
   3. C.$2m\frac{v_0}{x_0}$
   4. D.$\frac{2}{3}m{\left(\frac{v_0}{x_0}\right)}^2$
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   Answer: D

2. Q352012 · 7 May 2012 · Shift 1

   A particle gets displaced by $\Delta \vec{r}=(2\hat{i}+3\hat{j}+4\hat{k})\mathrm{m}$ under the action of a force $\vec{F}=(7\hat{i}+4\hat{j}+3\hat{k})$. The change in its kinetic energy is

   1. A.$38\mathrm{J}$
   2. B.$70\mathrm{J}$
   3. C.$52.5\mathrm{J}$
   4. D.$126\mathrm{J}$
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   Answer: A