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,
