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Section B (Paragraph / Problem Type)

Answer all questions in a paragraph of about half a page to one page, each correct answer carries a

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maximum of 5 marks.

A5kg. mass moves under the influence of a force F = (4077 - 3tj ) N, wheret is the time in seconds.

(IN = 1 Newton). It starts at rest from the origin at ¢ = 0. Find:
(a) Itsvelocity. (b) Its position.
(c) r xv, for any later time.

A Mass m is whirled on the end of a string length R. The motion is in a vertical plane in the
gravitational field of the earth. The forces on m are the weight W down, and the string force T
towards the centre. The instantaneous speed is v, and the string makes angle 8 with the horizontal.

Find the T and the tangential acceleration at this instant.
Solve the equation of simple harmonic motion.

A uniform rope of mass m and length J 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

Write a note on small oscillation in a bound system

Show that if the total force on a system of particles is zero, the torque on the system is the same

around all origins..

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

Find the force on each car ?

(Ceiling - 30)

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