A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. The fragments having equal masses fly off along mutually perpendicular direction with speed v. What will be the speed of the third (lighter) fragment ?
A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. At what height will the ball lose contact with surface of the sphere ?
Two identical cylindrical vessels, with their bases at the same level, each contain a liquidof density ρ. The height of liquid in one vessel in h1 and that in the other is h2. The area of either base is A. What is the work done by gravity in equalizing the levels when the vessels are interconnected ?
A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r.
The circuit can be diagrammatically shown as
From the circuit, we see that the current in the circuit would be equal to
Thus, the power would be equal to
So, for maximum power
Thus, we get
Hence, R + r − 2R = 0
So, r = R, hence proved.
A radioactive isotope X with half life 1.5x 109 yr decays into a stable nucleus Y. A rock sample contains both elements X and Y in ratio 1 : 15. Find the age of the rock.