Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
$\frac{1}{2}\,m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$\frac{1}{2}\,{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{\kern 1pt} {t^2}$
$\frac{1}{2}\,m\,\frac{v^2}{{{t^2_1}}}{\kern 1pt} {t^2}$
Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision
A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$ $(g = 10\, m/s^2$)
Three particles of masses $10g, 20g$ and $40g$ are moving with velocities $10\widehat i,10\widehat j$ and $10\widehat k$ $m/s$ respectively. If due to some mutual interaction, the first particle comes to rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is
System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5\, kg$ block, when $2\, kg$ block leaves the contact with ground is : (take force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)