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A particle acted upon by constant fo...

A particle acted upon by constant forces `4hati +hatj- 4 hatk` and `3hati + hatj - hatk` is displacment from the point `hati+ 2hatj+ hatk` to point `5hati + 4hatj +hatk`.Total work done by the forces in SI unit is :

A

20

B

40

C

50

D

30

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `vecF_1=4hati+hatj-3hatk,vecF_2=3hati+hatj-hatk`
`vecr_1=hati+2hatj+3hatk, vecr_2=5hati+4hatj+hatk`
Displacement , `vecr=vecr_2-vecr_1`
`=(5hati+4hatj+hatk)-(hati+2hatj+3hatk)=4hati+2hatj-2hatk`
Work done by the forces,
`W=[vecF_1+vecF_2].vecr`
`=[(4hati+hatj-3hatk)+(3hati+hatj-hatk)].(4hati+2hatj-2hatk)`
`=(7hati+2hatj-4hatk).(4hati+2hatj-2hatk)=28+4+8=40 J`
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