A batsman hits a ball of mass 0.2 kg straight towards the bowler without changing its initial speed of $$6 \mathrm{~m} / \mathrm{s}$$. What is the impulse imparted to the ball?

There are four convex lenses $$L_1, L_2, L_3$$ and $$L_4$$ of focal length $$2,4,6$$ and 8 cm, respectively. Two of these lenses from a telescope of length 10 cm and magnifying power 4. The objective and eye lenses are respectively

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is