Question

Two masses 2m and m are whirled in a horizontal circle.the radius of path of 2m is r and m is 2r.the ratio of tension of two strings are

Answer 1

Answer:

4:1

Explanation:

refer attached image

Answer 2

Answer:

The ratio of tension of two strings are 4:1

Explanation:

In this question

We have been given that,

Two masses 2m and m are whirled in a horizontal circle;

Radius of path of 2m is r and Radius of path of m is r.

We need to  find the ratio of tension of two strings.

As we know  Tension of the string in circular motion is given by $\frac{m\times v^{2}}{r}$

Where m is the mass,v is the velocity and r is the radius of the circular path.

Tension of the string with mass 2m and radius r is given by $\frac{2mv_{1}^{2}}{r}$

Tension of the string with mass m and radius 2r is given by $\frac{mv_{2}^{2}}{2r}$

Now, assuming both the strings be whirled with the same velocity

$T_{1}=\frac{2mv^{2}}{r}$

$T_{2}=\frac{mv{2}}{2r}$

On dividing $T_{1}\ by\ T_{2}\ we\ get$

$\frac{T_{1}}{T_{2}}=\frac{\frac{2mv^{2}}{r}}{\frac{mv^{2}}{2r}}$

$\frac{T_{1}}{T_{2}}=\frac{\frac{2m}{r}}{\frac{m}{2r}}$

$\frac{T_{1}}{T_{2}}=\frac{4}{1}$

Tension of both the strings will be in the ratio 4:1