Question 177: Gravitation

Question

The maximum and minimum distances of a comet from the Sun are 1.6 $$	imes$$ 1012 m and 8.0 $$	imes$$ 1010 m respectively. If the speed of the comet at the nearest point is 6 $$	imes$$ 104 ms$$-$$1, the speed at the farthest point is :

Accepted Answer

v
1
= 6 $$	imes$$ 10
4
m/s
Let point 1 is nearest point,
and point 2 is farthest point.
Given, r
1
= 8 $$	imes$$ 10
10
m & r
2
= 1.6 $$	imes$$ 10
12
m
By angular momentum conservation
L
1
= L
2
mr
1
v
1
= mr
2
v
2
$$ \Rightarrow $$ v
2
= $${{{r_1}{v_1}} \over {{r_2}}}$$
$$ 	herefore $$ v
2
= $${{8 	imes {{10}^{10}} 	imes 6 	imes {{10}^4}} \over {1.6 	imes {{10}^{12}}}}$$
$$ \Rightarrow $$ v
2
= 3.0 $$	imes$$ 10
3
m/s

Answer

3.0 $$	imes$$ 103 m/s

Answer

6.0 $$	imes$$ 103 m/s

Answer

1.5 $$	imes$$ 103 m/s

Answer

4.5 $$	imes$$ 103 m/s

Gravitation

The maximum and minimum distances of a comet from the Sun are 1.6 $\times 1012 m and 8.0 \times 1010 m respectively. If the speed of the comet at the nearest point is 6 \times 104 ms-$1, the speed at the farthest point is :

Choose the correct answer: