A metal sphere I hung by a string fixed to a wall. The forces acting on the sphere are shown in fig. Which of the following statements is `//` are correct ?

(a) `N+T+ W =0`
( b) `T^(2) = N^(2) + W^(2)`
( c ) `T = N + W `
(d) `N = W tan theta `

Options

A. `vec(N)+vec(T)+vec(W)=0`
B. `T^(2)+N^(2)+W^(2)=0`
C. `T=N+W`
D. `N=W sin theta`

Answer

A

Explanation

For equilibrium `alpha` sphere, vector sum of all the forces must be zero. Hence `vec(N)+vec(T)+vec(W)=0`. Also by componating. `T cos theta=W` and `T sin theta=N`. Hence `T^(2)=W^(2)+N^(2)` and `N=W tan theta`