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A solid cone hanges from a frictionless ...

A solid cone hanges from a frictionless pivot at the origin `O`, as shown. If `hat i, hat j` and `hat k` are unit vectors, and `a,b`, and `c` are positive constants, which of the following forces `F` applied to the rim of the cone at a point `P` results in a torque `tau` on the cone with a negative component `tau_(Z)` ?
.

A

`F = a hat k, P` is `(0,b, - c)`

B

`F = -a hat k, P` is `(0, -b,-c)`

C

`F = a hat j, P` is `(-b, 0, -c)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
C
`vec tau = vec r xx vec F`
for `( c)`
`vec tau = (- b hat i- o hat k) xx (a hat j) rArr vec tau = - ab hat k`.
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