A bob of mass m , suspended by a string of length l 1 , is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m , suspended by a string of length l 2 , which is initially at rest. Both the…

Question

A bob of mass m , suspended by a string of length l 1 , is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m , suspended by a string of length l 2 , which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l 1 l 2 is

Aicharya · Accepted Answer

As shown in the figure shown above, the minimum speed required by the bob of mass

m

attached to the string of length

l_{1}

in order to complete the full circle is

\sqrt{5 g l_{1}}

.

When the bob goes to the highest point, its speed becomes

\sqrt{g l_{1}}

. Here, it strikes with the identical mass, which is tied to the string of length

l_{2}

. The speed delivered to the object is

\sqrt{g l_{1}}

. This should be equal to

\sqrt{5 g l_{2}}

so that this bob could complete a full circle.

\sqrt{g l_{1}} = \sqrt{5 g l_{2}}

\Rightarrow g l_{1} = 5 g l_{2}

\Rightarrow \frac{l_{1}}{l_{2}} = 5

A bob of mass m , suspended by a string of length l 1 , is given a minimum velocity required to complete a…

Solution