When 2 pulleys are considered such that tension acting in 1st pulley is twice that of in the 2nd pulley , then why is the acceleration of the 1st pulley is half of that of 2nd pulley?

T1= 2T2

a2=2a1

Question

When 2 pulleys are considered such that tension acting in 1st pulley is twice that of in the 2nd pulley , then why is the acceleration of the 1st pulley is half of that of 2nd pulley? T1= 2T2 a2=2a1

Aman Bansal · Answer

Dear Naman,

he blocks are connected by a taut string. Hence, their accelerations are same. Let us assume directions of accelerations as shown in the figure. Also, let the magnitude of accelerations be “a”.

**Figure 2**
Static pulley system

Free body diagram of body of mass 10 kg

The external forces are (i) weight of block, 10g, and (ii) tension, T, in the string.

**Figure 3**
Free body diagram

\sum F y = T - 10 g = 10 a \Rightarrow T - 10 x 10 = 10 a \Rightarrow T = 100 + 10 a

Free body diagram of body of mass 20 kg

The external forces are (i) weight of block, 20g, and (ii) tension, T, in the string.

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When 2 pulleys are considered such that tension acting in 1st pulley is twice that of in the 2nd pulley , then why is the acceleration of the 1st pulley is half of that of 2nd pulley? T1= 2T2 a2=2a1

When 2 pulleys are considered such that tension acting in 1st pulley is twice that of in the 2nd pulley , then why is the acceleration of the 1st pulley is half of that of 2nd pulley?

T1= 2T2

a2=2a1

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