A mass m rotating freely in a horizontal circle of radius 1m on a frictionless smooth table supports a stationary mass 2m , attached to the other end of the string passing through a smooth hole O in table, hanging vertically. Find the angular velocity of rotation.

Question

A mass m rotating freely in a horizontal circle of radius 1m on a frictionless smooth table supports a stationary mass 2m , attached to the other end of the string passing through a smooth hole O in table, hanging vertically. Find the angular velocity of rotation. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-458x0eypjla0dixq.jpg" /> (A) √5 g (B) √3 g (C) √2 g (D) √g

Tardigrade Admin · Accepted Answer

Tension in string balances gravity of mass 2m and provide centripetal acceleration to mass m . T=2mg=mrω 2 ⇒ ω =√(2 g/r)=√2 grads- 1

Q. A mass $m$ rotating freely in a horizontal circle of radius $1 m$ on a frictionless smooth table supports a stationary mass $2 m$ , attached to the other end of the string passing through a smooth hole $O$ in table, hanging vertically. Find the angular velocity of rotation.

$5 g$

$3 g$

$2 g$

$g$

Tension in string balances gravity of mass $2 m$ and provide centripetal acceleration to mass $m$ .
$T = 2 m g = m r ω^{2}$
$\Rightarrow ω = \frac{2 g}{r} = 2 g r a d s^{- 1}$

Q. A mass m rotating freely in a horizontal circle of radius 1m on a frictionless smooth table supports a stationary mass 2m , attached to the other end of the string passing through a smooth hole O in table, hanging vertically. Find the angular velocity of rotation.

5g​

3g​

2g​

g​

Tension in string balances gravity of mass 2m and provide centripetal acceleration to mass m . T=2mg=mrω2 ⇒ω=r2g​​=2g​rads−1

Q. A mass $m$ rotating freely in a horizontal circle of radius $1 m$ on a frictionless smooth table supports a stationary mass $2 m$ , attached to the other end of the string passing through a smooth hole $O$ in table, hanging vertically. Find the angular velocity of rotation.

$5 g$

$3 g$

$2 g$

$g$

Tension in string balances gravity of mass $2 m$ and provide centripetal acceleration to mass $m$ .
$T = 2 m g = m r ω^{2}$
$\Rightarrow ω = \frac{2 g}{r} = 2 g r a d s^{- 1}$