Question

A body is moving around sun in an elliptical orbit.The maximum and minimum distance are $3\times {10}^{12}mand2\times {10}^{10}m$. The velocity at minimum distance is $2\times {10}^{7}m/sec$. Find the velocity of the body at maximum distance.

• A. $1.33\times {10}^{5}m/sec$
• B. $13.3\times {10}^{5}m/sec$
• C. $133\times {10}^{5}km/sec$
• D. $13.3\times {10}^{5}km/sec$

Answer 1

Answer: (A)

$1.33\times {10}^{5}m/sec$

As in the absence of external torque, $L$ is conserved.

i-e, $mvr=constant$

$v_{max}{r}_{max}=v_{min}{r}_{min}$

$v_{max}\times 3\times {10}^{12}=2\times {10}^7\times 2\times {10}^{10}$

$⟹v_{max}=1.33\times {10}^{5}m/sec$