Tension in string and accelerations of blocks:
Find out the tension in string and accelerations of blocks A and B having weights 200N and 50N respectively, connected by the string and frictionless and weightless pulleys as shown in the figure given below.
Sol: Given,
Weight of block A = 200N Weight of block B = 50N
As pulley is smooth, tension in the string will be same throughout
Let, T = Tension in string a = Acceleration of block B
Then acceleration of block A will be equal to half acceleration of block B. Acceleration of block
A = a/2 ...(i)
As weight of block is more than weight of block B, block A will move downwards whereas block B will move upwards.
Consider motion of block B,
Net force = T - 50 ...(ii)
As Net force, F = ma
T - 50 = (50/9.81) a
T - 50 = 5.1a ...(iii)
Consider motion of block A,
Net force = 200- 2T ...(iv)
As Net force, F = ma
200- 2T = (200/9.81)(a/2)
200- 2T = 10.19a
100 - T = 5.1a ...(v)
Add the equation (3) and (5)
50 = 10.19a
a = 4.9m/sec^{2 } .......ANS
Putting value of a in equation (5) we get
T = 75N .......ANS