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13. A uniform ladder of 4m length rests against a vertical wall with which it makes an
angle of 45°. The coefficient of friction between the ladder and the wall is 0.4 and
that between ladder and floor is 0.5. If a man, whose weight is one-half of the weight
of ladder, ascends it, how high will he be when the ladder slips?

14. An effort of 200N is required just to move a certain body up an inclined plane of
angle 15°, the force acting parallel to the plane. If the angle of inclination of the plane
is made 20° the effort required, again parallel to the plane is found to be 230N. Find
the weight of the body and the coefficient of friction.

SET 3

Each question carries 10 marks

15. For a reciprocating pump, crank OA rotates at a uniform speed of 300 rpm. The
length of crank and connecting rod are 12 cm and 50cm respectively. Find (1) the
angular velocity of the connecting rod AB and (ii) the velocity of piston when the
crank makes an angle 30° with the horizontal.

16. Two blocks A and B of weight 150N and 100N are released from rest on a 30°
inclined plane, when they are 15m apart. The coefficient of friction between the
upper block A and the plane is 0.2 and that between the lower block B and the plane
is 0.4. In what time block A reach block B? After they touch and move as a single
unit, what will be acceleration with which it will move down?

17. A spring stretches by 0.015m when a 1.75 kg object is suspended from its end. How
much mass should be attached to the spring so that its frequency of vibration is 3.0
Hz?

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