Question

In the arrangement shown in figure, friction is absent everywhere. Pulleys and strings are ideal.
Acceleration of block A is 59/13 Acceleration of block B is 2g/ 13
Tension in the string is 3mg /13 Acceleration of A with respect to B is 7g/ 13​

Answer 1

Given:

Three blocks with masses 2m, 2m, and m

3 ideal pulleys and ideal strings

To find:

Tension in the string

Solution:

Let the tension in the string be T.

Since the strings are ideal and there is no friction, the tension is the same all over the string.

Equation for Block A:

2T - 0 = 2m a₁                               - 1

Equation for Block B:

T - 0 = 2m a₂                                 -2

Equation for block C:

mg - T = m a₃                                  -3

From above , a₁ = 2 a₂ = 2 a₃         -4

Solving equations 1, 2, 3, and 4

T=  mg - m a₃

(From equtaion 4 and 2, a₃ = T/2m)

So, T= mg - T/2

3T = 2mg

or T = 2mg/3

Hence the tension in the string is 2mg/3 N.