In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor, throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be
$h\left( {1 + \frac{m}{M}} \right)$
$\left( {1 + \frac{M}{m}} \right)h$
$h$
$\frac {m}{M}h$
Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat i +\hat j+ \hat k$ and $-\hat i -\hat j -\hat k$ respectively would have the centre of mass at
Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ................
Four masses are fixed on a massless rod as shown in Fig. The moment of inertia about the axis $P$ is about ....... $kg-m^2$
The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta (t) = 2t^3 -6t^2$. The torque on the wheel becomes zero at $t$ $=$ ........ $\sec.$
Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$ ) is: (Assume disc is of negligible mass)