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/sec²                                                                                                     .......ANS

Putting value of a in equation (5) we get

T = 75N                                                                             .......ANS