There are n elastic balls placed on a smooth horizontal plane. The masses of the balls are $$\mathrm{m}, \frac{\mathrm{m}}{2}, \frac{\mathrm{m}}{2^{2}}, \ldots \frac{\mathrm{m}}{2^{\mathrm{n}-1}}$$ respectively. If the first ball hits the second ball with velocity $$\mathrm{v}_{0}$$, then the velocity of the $$\mathrm{n}^{\text {th }}$$ ball will be,
A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $$\overrightarrow r $$ denote the linear momentum, angular momentum and position vector of the particle (from focus O) respectively at a point A, then the direction of $$\overrightarrow \alpha $$ = $$\overrightarrow p $$ $$\times$$ $$\overrightarrow L $$ is along.
A body of mass m is thrown with velocity u from the origin of a co-ordinate axes at an angle $$\theta$$ with the horizon. The magnitude of the angular momentum of the particle about the origin at time t when it is at the maximum height of the trajectory is proportional to
Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC in g-cm2 units will be
