Question

A large free mass M and a small mass m are connected to a string such that m moves in horizontal circle. Length of string is l and θ is the angle this length makes with vertical. The frequency of rotation of mass m so that M remains at rest is

• A. $2 \pi \sqrt { \frac { \mathrm { ml } } { \mathrm { Mg } } }$
• B. $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { mg } } { \mathrm { Ml } } }$
• C. $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { ml } } { \mathrm { Mg } } }$
• D. $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { Mg } } { \mathrm { ml } } }$

Answer 1

Answer: (D)

$\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { Mg } } { \mathrm { ml } } }$

Answer 2

Here T = Mg and T cos θ = Mg

Also T sin θ = mω²l sin θ ( radius = l sin θ)

i.e., T = mω²l

or Mg = mω²l i.e., ω = $\sqrt { \frac { \mathrm { Mg } } { \mathrm { ml } } }$

i.e., 2πv = $\sqrt { \frac { \mathrm { Mg } } { \mathrm { ml } } }$ i.e., v = $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { Mg } } { \mathrm { ml } } }$