## Friday, October 09, 2009

### AIPMT 2009 Multiple Choice Questions on Work, Energy & Power

How strange is the lot of we mortals! Each of us is here for a brief sojourn; for what purpose we know not, though sometimes sense it. But we know from daily life that we exist for other people first of all for whose smiles and well-being our own happiness depends.

–Albert Einstein

Three questions from the section ‘work, energy & power’ were included in the AIPMT 2009 question paper. Here are those questions with solution:

(1) A block of mass M is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

(1) 2 Mg/k

(2) 4 Mg/k

(3) Mg/2k

(4) Mg/k

If x is the maximum extension produced, we have

Mgx = ½ kx2, on equating the decrease in the gravitational potential energy of the mass M to the increase in the elastic potential energy of the spring.

Therefore, x = 2Mg/k

(2) A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (g = 10 ms–2)

(1) 30 J

(2) 40 J

(3) 10 J

(4) 20 J

The initial kinetic energy of the 1 kg mass is given by

½ mv2 = ½ ×1×202 = 200 J.

The gravitational potential energy of the 1 kg mass at its maximum height is given by

Mgh = 1×10×18 = 180 J.

The energy lost due to air friction is therefore equal to 200 – 180 = 20 J.

(3) An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

(1) mv2

(2) ½ mv2

(3) ½ m2v2

(4) ½ mv3

Mas of water flowing out per second through the hose is mv. Therefore, kinetic energy imparted per second to the water is ½ ×(mv)×v2 = ½ mv3 [Option (3)].

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