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Question

A particle in a certain conservative force field has a potential energy given by U=20xyz. The force exerted on it is?
  1. (20yz)^i(20xz)^j+(20xyz2)^k
  2. (20yz)^i+(20xz)^j+(20xyz2)^k
  3. (20yz)^i(20xz)^j(20xyz2)^k
  4. (20yz)^i+(20xz)^j(20xyz2)^k

A
(20yz)^i(20xz)^j+(20xyz2)^k
B
(20yz)^i(20xz)^j(20xyz2)^k
C
(20yz)^i+(20xz)^j+(20xyz2)^k
D
(20yz)^i+(20xz)^j(20xyz2)^k
Solution
Verified by Toppr

The correct option is A (20yz)^i+(20xz)^j+(20xyz2)^k

The potential energy function U(x) for a system in which a one - dimensional force F acts on a particle, we can find the force as
F(x)=dUdx=dUxdx+dUydx+dUzdx

Apply U=20xyz

=20yzi+20xzj20xyz2k

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