A body is dropped from a height $h$ . If it acquires a momentum $p$ just before striking the ground, then the mass of the body is
$\frac{p}{{\sqrt {2gh} }}$
$\frac{{{p^2}}}{{2gh}}$
$\frac{{2gh}}{p}$
$\sqrt {\frac{{2gh}}{p}} $
A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the inclined calculate
$(a)$ work done against gravity
$(b)$ work done against force of friction
$(c)$ increases in potential energy
$(d)$ increases in kinetic energy
$(e)$ work done by applied force
$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
A sphere is suspended by a thread of length $\ell $. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension
The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.
$(III)$ The mass of $R$ was greater than mass of $S.$
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