Question

In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and strings to be massless and smooth, the acceleration of block 'C' will be:
(A) Zero (B) 2.5 m/s2
(C) 10/7 m/s2 (D) 5/7 m/s2

Answer 1

For 10kg Block

ma + ma base 0 = mg - T

10(a+a base 0) = 100- 7 -- (1)

5kg Block

5 (a - a base 0) = T - 50 -- (2)

8 Kg Block

8 a = 2T - 80 -- (3)

Now we will solve 1 and 3

10 a + 10a base 0 = 100 - T

10 a - 10 a base 0 = 2T - 50

(20 base a = T + 50) x 2

40 a  = 2T + 100

8a = 2T - 80 from equation 3

32 a  = 20

a = 20/ 32 5/8 + 0.6 m/s^2

We will calculate the acceleration of Block C  which is 0.6m/s^2

x/10 = 0.6

or x = 6 m/s^2