Question

If the work done by the string on block A is W,
then work done by the string on the block B will
be
​

Answer 1

The answer of this question is (2)-w/2

Answer 2

The work done by the string on the block B is -W and option (1) is correct.

Explanation:

Given:

The work done by the string on block A is W.

To Find:

The work done by the string on the block B.

Formula Used:

Reference to attached picture.

By constraint relationship.

Suppose mass A moves by $x1$ distance and mass B moves up by $x2$distance. T is the tension in the string.

Work done by string on block A $=-T.\ x_{1}$    --------- formula no.01.

Work done by string on block B $=2T.\ x_{2}$   -------- formula no.02.

                               $x_{1} =2\ x_{2}$         ---------- formula no.03

Solution:

Reference to attached picture.

As given,the work done by the string on block A is W.

the work done by the string on block A = W.

Using the formula no.01.

Work done by string on block A $=-T.\ x_{1}$

$W=-T.\ x_{1}$

$x_{1}= - \frac{W}{T}$    --------  equation no.01.

Using the formula no.03.

$x_{1} =2\ x_{2}\\\ x_{2}=\frac{x_{1} }{2}$

Putting the value of $x1$ from equation no.01.

$\ x_{2}=\frac{(-\frac{W}{T}) }{2}$    

 $x_{2} =-\frac{W}{2T}$  ------------ equation no.02.

Using formula no.03.

Work done by string on block B $=2T.\ x_{2}$  

Putting the value of $x_{2}$ from equation no.02.

                                                      $=2T\times(-\frac{W}{2T})\\= -W$

Thus, the work done by the string on the block B is -W and option (1) is correct.      

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