A uniforbm beam 6m long weighing 4kg rest on supports at p and q placed left and right 10m from each end of the beam weights of mass 10kg and 8kg are placed near p and q respectively on each end of the beam . calculate the reactions at p and q ?

125N,95N Respectively

To calculate the reactions at points P and Q, we can use the principle of equilibrium. In order for the beam to remain in a state of equilibrium, the sum of the moments and forces acting on it must be equal to zero.

Let's break down the solution step by step:

1. Calculate the total weight acting on the beam:
The total weight of the beam is given as 4 kg. We can multiply this by the acceleration due to gravity (g = 9.8 m/s^2) to find the total weight acting downward:
Total weight = 4 kg × 9.8 m/s^2 = 39.2 N

2. Calculate the total weight acting at point P:
The beam is 10 m from point P, and there is a 10 kg weight placed near point P. We can treat the weight as acting at the center of mass of the beam, which is 3 m from point P. Therefore, the total weight acting at point P is:
Weight at P = (10 kg × 9.8 m/s^2) + (4 kg × 9.8 m/s^2 × 3 m / 6 m) = 98 N + 19.6 N = 117.6 N

3. Calculate the total weight acting at point Q:
Similar to point P, the beam is also 10 m from point Q, and there is an 8 kg weight placed near point Q. We can treat the weight as acting at the center of mass of the beam, which is 3 m from point Q. Therefore, the total weight acting at point Q is:
Weight at Q = (8 kg × 9.8 m/s^2) + (4 kg × 9.8 m/s^2 × 3 m / 6 m) = 78.4 N + 19.6 N = 98 N

4. Calculate the reactions at points P and Q:
Since the beam is in equilibrium, the sum of the forces acting on it must be zero. Therefore, the reaction force at point P should be equal to the total weight acting at point P (117.6 N), and the reaction force at point Q should be equal to the total weight acting at point Q (98 N).

Therefore, the reactions at points P and Q are:
Reaction at P = 117.6 N
Reaction at Q = 98 N