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NEET Physics Solved Question Paper 2011

Short Answer Type

41.
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 ?

We can represent in the form of a figure as

Now if we use the conservation of momentum we get

o = (2m) v cos 45° + (2m) v cos 45° + mv₁

So, v₁ = − 4 cos 45° v = − $2 \sqrt{2}$ , thus the velocity of the third part has a magnitude equal to $2 \sqrt{2} v$ , this makes an angle of 135° with respect to either of the three masses.

42.

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 ?

43.

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 ?

44.

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.

45.

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.