The figure shows a mass $$m$$ on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant $$k$$. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards right, then the speed of the block when the deformation in spring is $$x$$, will be
Body of mass M is much heavier than the other body of mass m. The heavier body with speed v collides with the lighter body which was at rest initially elastically. The speed of lighter body after collision is
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc
Three bodies having masses $$5 \mathrm{~kg}, 4 \mathrm{~kg}$$ and $$2 \mathrm{~kg}$$ is moving at the speed of $$5 \mathrm{~m} / \mathrm{s}, 4 \mathrm{~m} / \mathrm{s}$$ and $$2 \mathrm{~m} / \mathrm{s}$$ respectively along $$X$$-axis. The magnitude of velocity of centre of mass is