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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 ?

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.

The circuit can be diagrammatically shown as

From the circuit, we see that the current in the circuit would be equal to

$I = \frac{E}{R + r}$

Thus, the power would be equal to

$P = I^{2} R = {(\frac{E}{R + r})}^{2} R = \frac{E^{2} R}{{(R + r)}^{2}}$

So, for maximum power

$\frac{dP}{dR} = 0$

Thus, we get

$E^{2} [\frac{{(R + r)}^{2} - 2 R (R + r)}{{(R + r)}^{4}}] = 0$

Hence, R + r − 2R = 0

So, r = R, hence proved.

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.