1. Two monkeys of masses  and  are moving along a vertical rope which is light and inextensible, the former climbing up with an acceleration of  while the latter coming down with a uniform velocity of . Find the tension (in newtons).

A horizontal uniform rope of length , resting on a frictionless horizontal surface, is pulled at one end by force . What is the tension in the rope at a distance  from the end where the force is applied?

2. A smooth ring  of mass  can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley and carries a block  of mass  as shown in the figure. At an instant, the string between the ring and the pulley makes an angle  with the rod. The initial acceleration of the ring is

2. A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration  directed horizontally as shown in figure.

Other end of the string is pulled with constant acceleration  vertically. The tension in the string is equal to

A body of mass  is suspended by a staring of length  from the ceiling. A force  is applied horizontally at the mid-point. of the rope such that the top half of the rope makes an angle of  with the vertical. The value of  is

5. There are two blocks A and B in contact with vertical and horizontal smooth surfaces respectively, as shown in the figure. Acceleration of  and  are  and  respectively along their constrained direction of motions. Relation between  and  is (Assume  ).

5. In the figure acceleration of bodies A, B and C are shown with directions. Values  and  are w.r.t. ground whereas  is acceleration of block  w.r.t. wedge . Acceleration of block A w.r.t. ground is

A rocket is fired vertically from the earth with an acceleration of , where  is the gravitational acceleration. On an inclined plane inside the rocket, making an angle  with the horizontal, a point object of mass  is kept. The minimum coefficient of friction  between the mass and the inclined surface such that the mass does not move is :

8. Block  has a mass  and is released from rest when it is on top of wedge , which has a mass . Determine the extension of the spring of force constant  while  is sliding down on . Neglect friction :

10. A bead of mass  is located on a parabolic wire with its axis vertical and vertex at the origin as shown in the figure and whose equation is . The wire frame is fixed and the bead can slide on it without friction. The bead is released from point  on the frame from rest. The tangential acceleration of the bead when it reaches the position given by  is