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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 ?

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 ?

We know that if the ball looses contact at B, then from conservation of energy, we get

So, we get v² = 2gR (1 − cos θ) ...... (i)

Hence at point B, we have

$N + \frac{{mv}^{2}}{R} = mg \cos θ$

So, when the ball looses contact, the normal reaction becomes equal to zero, ie, N = 0

Hence, $\frac{{mv}^{2}}{R} = mg \cos θ$

This along with Eqn. (i), we get

v² = Rg cos θ = 2gR (1 − cos θ)

Hence, we have

2 − 2 cos θ = cos θ

So, cos θ = $\frac{2}{3}$

Hence the height from the ground would be equal to

h = R cos θ = $\frac{2 R}{3}$

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.