Center Of Mass - Mechanics - Physics Previous Year Questions

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.

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

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

A particle of mass m is projected at a velocity u, making an angle \(\theta\) with the horizontal (x-axis). If the angle of projection \(\theta\) is varied keeping all other parameters same, then magnitude of angular momentum (L) at its maximum height about the point of projection varies with \(\theta\) as,

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,

The position of the centre of mass of the uniform plate as shown in the figure is

A uniform rod \(\mathrm{AB}\) of length \(1 \mathrm{~m}\) and mass \(4 \mathrm{~kg}\) is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the \(\operatorname{rod} \mathrm{A}\) and \(\mathrm{B}\) are \(3 \mathrm{~m} / \mathrm{s}\) and \(4 \mathrm{~m} / \mathrm{s}\) respectively, as shown in the figure. Then which of the following statement(s) is/are correct?

The variation of density of a solid cylindrical rod of cross sectional area $\alpha$ and length $L$ is $\rho=\rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from one end $(x=0)$ is

A ball falls from a height $h$ upon a fixed horizontal floor. The co-efficient of restitution for the collision between the ball and the floor is ' $e$ '. The total distance covered by the ball before coming to rest is [neglect the air resistance]