Three monkeys are climbing upstairs. They can only move ahead if they eat a banana with the common factor of their numerator and denominator on it. Which of the three monkeys will be able to reach till the end?

A monkey of mass m climbs up to a rope hung over a fixed pulley. The opposite end of the rope is tied to a weight of mass M lying on a horizontal plane. Neglecting the friction, find the acceleration of both the bodies (relative to the plane) and the tension of the rope for the three cases: (i) The monkey does not move with respect to the rope (ii) The monkey moves upwards with respect to the rope with acceleration a. (iii) The monkey moves downwards with respect to the rope, with acceleration a.

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes anangle of 30^(@) with the ground. A monkey if makes an angle of 30^(@) with the ground. A monkey of mass 5kg climbs up the rope. The clamp can tolerate is vertical force of 40N only. the maximum accelration in upward direction with which the monkey can climb safety is (Neglect friciton and take g=10m//s^(2) )

A monkey is a reston a weightless rope which goes over a pulley and is tied to a bunch of bananas at the other end. The weight of the bunch of bananas isexactly the same as that of the monkey. The pulley is frictionless and weightless. The monkey starts to climb up the rope to reach the bananas. As he climbs, the distance between him and the bananas will

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of 30^(@) with the ground. A monkey of mass 5 kg climbs up the rope. The clamp can tolerate a vertical force of 40 N only. The maximum acceleration in upward direction with which the monkey can climb safely is: (neglect friction and take g=10m//s^(2))

Laila and Majnu are on a boat for a picnic. The boat is initially at rest. Laila has a big watermelon which she throws towards Majnu. The man catches the melon and eats half of it. He throws back the remaining half to Laila. She eats the half of the melon that she receives & throws the remaining part to Majnu. Majnu again eats half of what he receives and returns the remaining part back to Laila. This continues till the melon lasts. The two are sitting at the two ends of the boat which has a length L. Combined mass of the boat and the two lovers is M_(0) and the mass of the water melon is M. Assume that the boat can move horizontally on water without any resistive force. Find the displacement of the boat when the watermelon gets finished.

A 12kg monkey climbs a light rope.The rope passes over a pulley and is attached to a 16kg bunch of bananas resting on floor. Mass and friction in the pulley are negligible so that the pulley's only effect is to reverse the direction of the rope. What is the maximum acceleration the monkey can have without lifting the bananas ? (Take g=10m//s^(2) )