A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 ms/s A plumb bob is suspended from the roof of the car by a light rigid rod of length 1m. The angle made by the rod with the track is (Take g= 10m/`s^(2)`

Options

A. zero
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

C

Explanation

The force acting on the bob are (i) its weight mg and (ii) centripetal force `F_(c) = (mv^(2))/(r)` . Resolving these force into components along and perpendicular to rod (see figure ) ,we have (since the bob is in equilibrium )
T = mg cos `theta + F_(c) "sin" theta " " ...... (i) `
and mg sin `theta = F_(c) "cos" theta " " ........ (ii)`
From Eq. (ii)
mg sin `theta = (mv^(2))/(r) "cos" theta`
`implies "tan" theta = (v^(2))/(rg) = ((10)^(2))/(10 xx 10) = 1` which gives `theta = 45^(@)`