Two bodies of masses m 1 = 5 kg and m 2 = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m 1 will be : [Take g = 10 m s - 2 ] ​​​​​​​

Step-by-step solution

The forces acting on two masses are shown below. Here, N is normal to the incline and tension T along the string up the incline. As the string and the pulley are all light and smooth, the tension in the string is uniform everywhere. ​​​​​​​ For equilibrium condition, forces should add to zero. Thus, equating, m 2 g = m 1 g sin θ ⇒ sin θ = m 2 m 1 = 3 5 and cos θ = 4 5 Normal force on m 1 is N = m 1 g cos θ = 5 g cos θ = 5 × 10 × 4 5 = 40 N