Two forces of magentude 7 newton and 5 newton act on a particle at an angle `theta` can have any value . The minimum magnitude of the resultant forces is :

Options

A. 5 newton
B. 8 newton
C. 12 newton
D. 2 newton

Answer

D

Explanation

Let `|vecF_(1)| = 7 and |vecF_(2)|=5`
`" "|F_(1) + F_(2)|= sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2) cos theta)`
`" "= sqrt(7^(2) + 5^(2) + 2xx7xx5 cos theta)`
`" "= sqrt(7^(2) + 5^(2) -70)=20`
(Minimum value of the `cos theta = -1`)