Potential energy for a conservative force →F is given by U(x,y)=cos(x+y). Force acting on a particle at position given by coordinates (0,π4) is
A
−1√2(^i+^j)
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B
1√2(^i+^j)
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C
[12^i+√32^j]
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D
[12^i−√32^j]
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Solution
The correct option is B1√2(^i+^j) We know, Fx=−dUdx
and Fy=−dUdy ∴Fx=−dUdx=−ddxcos(x+y)=sin(x+y)∴Fx at (0,π4) is =sin(0+π4)=1√2
Similarly, Fy=−dUdy=−ddycos(x+y)=sin(x+y)∴Fy at (0,π4) is =sin(0+π4)=1√2 ⇒→F=Fx^i+Fy^j=1√2^i+1√2^j=1√2(^i+^j)