Question

A string of length `l` is fixed at one end and carries a mass 'm' at the other end. The mass is revolving along a horizontal circle of radius 'r' making 'θ' as the semi-vertical angle of cone and `(1/pi)` revolutions per second around the vertical axis through fixed end. The tension in the string is ______.

Options

• 2 ml

• 8 ml

• 4 ml

• 16 ml

Answer 1

A string of length `l` is fixed at one end and carries a mass 'm' at the other end. The mass is revolving along a horizontal circle of radius 'r' making 'θ' as the semi-vertical angle of cone and `(1/pi)` revolutions per second around the vertical axis through fixed end. The tension in the string is 4 ml.

Explanation:

Frequency `f=1/pi` rps, ω = 2πf = `2pixx1/pi  `= 2 rad/s

In a conical pendulum, the horizontal component of the tension Tsinθ provides the centripetal force.

∴ Tsinθ = mrω²

but r = Lsinθ and ω² = 4

∴ T = 4mL