# NCERT Physics Class 11 Exemplar Ch 6 Work Energy and Power Part 7

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Q 44. A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of by a force of 10 N parallel to the inclined surface. The coefficient of friction between block and the incline is 0.1. If the block is pushed up by along the incline, calculate

(a) Work done against gravity

(b) Work done against force of friction

(c) Increase in potential energy

(d) Increase in kinetic energy

(e) Work done by applied force.

Ans:

(a)

(b)

(c)

(d)

(e)

Q 45. A curved surface is shown in. Q the portion BCD is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from A which is at a slightly greater height than C.

With the surface AB, ball 1 has large enough friction to cause rolling down without slipping; ball 2 has a small friction and ball 3 has a negligible friction.

(a) For which balls is total mechanical energy conserved?

(b) Which ball (s) can reach D?

(c) For balls which do not reach D, which of the balls can reach back A?

Ans:

(a) Energy is conserved for balls 1 and 3.

(b) Ball 1 acquires rotational energy, ball 2 loses energy by friction.

They cannot cross at C. Ball 3 can cross over

(c) Ball 1, 2 turn back before reaching C. Because of loss of energy, ball 2 cannot reach back to A. Ball 1 has a rotational motion in “wrong” sense when it reaches B. It cannot roll back to A, because of kinetic friction.

Q 46. A rocket accelerates straight up by ejecting gas downwards. In a small time interval, it ejects a gas of mass at a relative speed u. Calculate KE of the entire system at and and show that the device that ejects gas does work in this time interval (neglect gravity).

Ans:

Rocket Gas

(By work –Energy theorem)

Since

Q 47. Two identical steel cubes (masses, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel

Ans:

Hooke’s law:

Where A is the surface area and L is length of the side of the cube. If k is spring or compression constant. Then

Initial

Final

Q 48. A balloon filled with helium rises against gravity increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect viscous drag of air and assume that density of air is constant.

Ans:

Let denote respectively the mass. Volume and density of helium balloon and be density of air Volume V of balloon displaces volume V of air.

So. So, (1)

Integrating with respect to t.

(2)

It the balloon rises to a height h, from, we get

(3)

From Eqs. (3) and (2).

Rearranging the terms.

So, as the baloon goes up, an equal volume of air comes down, increase in PE and KE of the baloon is at the cost of PE of air [which comes down].