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Two skaters have weight in the ratio 4:5...

Two skaters have weight in the ratio `4:5` and are 9m 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

A

`5:4`

B

`4:5`

C

`25:16`

D

`16:25`

Text Solution

Verified by Experts

The correct Answer is:
A
Acceleration of the skaters will be in the ratio
`(F)/(4):(F)/(5) or 5:4`
Now according to the problem, `s=0+1/2at^(2)` we get
`(s_1)/(s_2)=(a_1)/(a_2) = 5/4`.
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Knowledge Check

  • Which of the following statements is true ? (i) A car of mass M is tied by one end of a massless rope of length 10 m . The other end of the rope is in the hands of a man of mass M . The entire system is on a smooth horizontal surface.The man is at x = 0 and the cart at x = 10 m . If the man pulls the cart by the rope, the man and the cart will meet at the point x = 5 m . (ii) Two spherical bodies of mass M and 5 M and radii R and 2 R , respectively , are released in free space with initial separation between their centers equal to 12 R . If they attract each other due to the gravitational force only , then the distance covered by the smaller body just before collision is 7.5 R . (iii) Two skaters A and B , having masses 40 kg and 60 kg , respectively stand facing each other 10 m apart on a horizontal smooth surface. They pull on a rope stretched between them , the distance covered by A , when skaters meet is 6 m . (iv) A ballon (mass M) is attached to light rope of length L . To the other end of the rope a boy (mass m) is hanging in air. The system is at rest. The distance travelled by the balloon (in downward direction) when the boy touches the ballon is (ML)/(M + m) .

    A
    `(i),(ii)`
    B
    `(i) , (ii) ,(iii)`
    C
    `(iii) ,(iv)`
    D
    all of the above

  • Two skaters A and B of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far each moved when they meet?

    A
    Both have moved 3 metres.
    B
    A moves 2.5 metres and B moves 3.5 metres.
    C
    A moves 3.5 metrs and B moves 2.5 metres.
    D
    A moves 2 metres and B moves 4 metres.

  • A cart of mass M is tied to one end of a massless rope of length 10 m . The other end of the rope is in the hands of a man of mass M . The entire system is on a smooth horizontal surface. The man is at x=0 and the cart at x=10 m . If the man pulls the cart by the rope, the man and the cart will meet at the point

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    they will never meet
    B
    `x=10 m`
    C
    `x=5 m`
    D
    `x=0`
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