Two spheres A and B of equal mass lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time $t$ A impinges on B. If $e$ is the coefficient of restitution, the second impinge will occur after a time

\frac{2 t}{e}

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\frac{t}{e}

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\frac{π t}{e}

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\frac{2 π t}{e}

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Solution

The correct option is A $\frac{2 t}{e}$
The time taken for covering distance depends on the relative velocities between the bodies.
Now, as per question,
$π r = t u$
Using equation of e,
$e = (v_{2} - v_{1}) / u \Rightarrow (v_{2} - v_{1}) = u e$
time required $= 2 π r / u e = 2 t / e$ .

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Two spheres A and B of equal mass lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time t A impinges on B. If e is the coefficient of restitution, the second impinge will occur after a time

The correct option is A 2teThe time taken for covering distance depends on the relative velocities between the bodies.Now, as per question,πr=tuUsing equation of e,e=(v2−v1)/u⇒(v2−v1)=uetime required =2πr/ue=2t/e.

Two spheres A and B of equal mass lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time $t$ A impinges on B. If $e$ is the coefficient of restitution, the second impinge will occur after a time

The correct option is A $\frac{2 t}{e}$
The time taken for covering distance depends on the relative velocities between the bodies.
Now, as per question,
$π r = t u$
Using equation of e,
$e = (v_{2} - v_{1}) / u \Rightarrow (v_{2} - v_{1}) = u e$
time required $= 2 π r / u e = 2 t / e$ .