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  • A particle moves from point (0,0) to point (9,9) by two paths under a constant force.  Path 1 is OP and path 2 is OQP as shown in the diagram. If work done by both paths is <img alt=

A particle moves from point (0,0) to point (9,9) by two paths under a constant force.  Path 1 is OP and path 2 is OQP as shown in the diagram. If work done by both paths is W _1  and W _2 then 

Option: 1

W _1 = W_2


Option: 2

W_1 = 2 W_2


Option: 3

W_ 2= 2 W_1


Option: 4

W_ 2 = 4 W_1


Answers (1)

best_answer

As we have learned

Work done is path independent -

It depends upon initial and final position

- wherein

When force is constant.

 

 For path OP 

W_1 = \vec F . \vec S

\vec F = (3 \hat i + 4 \hat j ) \: \: \: \: s = a \hat i + a \hat j

F = 3a + 4 a = 7a J

For path OQP 

W _2 = W_{ OQ} + W_{QP }

W _2 =\vec F . \vec { OQ} + \vec F \vec { QP }

= ( (3 \hat i + 4 \hat j) .a\hat i ) + ( (3 \hat i + 4 \hat j) .a\hat j )\\ = 3a + 4a = 7 a

W _1 = W_2

 

 

 

 

 

 

 

 

 

 

Posted by

vinayak

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