First slide

Law of conservation of momentum and it's applications

Question

Two skaters have weight in the ratio 4 : 5 and are 9 m apart, on a smooth frictionless surface. They pull on a rope stretched between them. The ratio of the distance covered by them when they meet each other will be

Moderate

A

5:4
B

4:5
C

25:16
D

16:25

Solution

Acceleration of the skaters will be in the ratio
$a_{1} : a_{2} = \frac{F}{4} : \frac{F}{5} or 5 : 4$
Here F is the tension in string.
Now according to the problem, $s = 0 + \frac{1}{2} a t^{2}$ , we get
$\frac{s_{1}}{s_{2}} = \frac{a_{1}}{a_{2}} = \frac{5}{4}$

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