Center of Mass · Physics · WB JEE

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]

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

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,

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

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?