# Find the tension in the string, and the value of m, in the following question. Two particles, P and Q, of mass 2 kg and m kg respectively, are connected by a light inextensible string. Particle P is held on a smooth horizontal table. The string passes over a smooth pulley R fixed at the edge of the table, and Q is at rest vertically below R. when P is released the acceleration of each particle has a magnitude 0.81 ms^2. Find the tension in the string and the value of m. (g= 9.81 m/s^2, and friction is negligible).

In the question, a body P of mass 2 kg is placed on a table which has a horizontal frictionless surface. It is connected to one end of a string. The string passes over a pulley at the edge of the table and on the other end hangs a body Q with a mass m.

On releasing the bodies, they move with an acceleration equal to 0.81 m/s^2.

The body Q is being pulled downwards with a force equal to m*g. As g is given as 9.81, the force is 9.81*m. The force creates a tension in the string equal to m*g = 9.81*m

This tension moves the other body P which has a mass equal to 2 kg.

Equating the acceleration of the body to the force applied, we get the relation:

9.81*m = 2*0.81

=> m = 2*0.81 / 9.81

=> m = 0.165 kg

The body Q that is suspended freely at one end of the string has a mass 0.165 kg. The tension in the string is equal to 1.62 N.

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