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14.

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Section B (Paragraph / Problem Type)

Answer at least five questions.

Each question carries 5 marks.

All questions can be attended.
Overall Ceiling 25.

A5kg mass moves under the influence of a force F = (47 27 - 8 j ) N, wheret is the time in seconds,
(1N = 1 Newton). It starts at rest from the origin att = 0. Find:

(a) Its velocity ;
(b) Its position ; and
(c) 7 xv, for any later time.

State and prove parallel axis theorem. Apply it to obtain the moment of inertia of a thin stick about
its end.
A uniform rope of mass m and length / is attached to a block of mass M. The rope is pulled with

force F, Find the tension at distance x from the end of the rope. Neglect gravity.

Analyze the molecular vibration of a diatomic molecule and calculate the fundamental frequency.
Draw the Potential Energy curve.

Show that :

(a) Ifthe total linear momentum of a system of particles is zero, the angular momentum of the

system is the same around all origins.

(b) Show that if the total force on a system of particles is zero, the torque on the system is the
same around all origins.

A loaded spring gun, initially at rest on a horizontal frictionless surface, fires a marble at angle of
elevation 9 .The mass of the gun is M, the mass of the marble is m, and the muzzle velocity of the
marble (the speed with which the marble is ejected, relative to the muzzle) is vy. What is the final
motion of the gun ?

Three freight cars each of mass M are pulled with force F by a locomotive. Friction is negligible.

Find the force on each car ?

(5 x 5 = 25 marks)

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