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Two masses m1 and m2 are connected by li...

Two masses m1 and m2 are connected by light string, which passes over the top of a smooth plane inclined at 30º to the horizontal, so that one mass rests on the plane and the other hangs vertically as shown in fig. It is found that m1, hanging vertically can draw m2 up the full length of the plane in half the time in which m2 hanging vertically draws m1 up. Find m1/m2 . Assume pulley to be smooth-

A

`2/3`

B

`3/2`

C

`4/7`

D

`7/4`

Text Solution

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The correct Answer is:
B
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Two masses M_(1) and M_(2) are connected by light string, which passes over the top of a smooth plane inclined at 30^(@) to the horizontal, so that one mass rests on the plane and the other hangs vertically as shown in figure. It is found that M_(1) , hanging vertically can draw M_(2) up the full length of the plane in half the time in which M_(2) hanging vertically draws M_(1) up. Find M_(1)//M_(2) . Assume pulley to be smooth. Initially at time t = 0 smooth masses M_(1) = 15 kg and M_(2) = 10 kg are held at rest and then they released. if after one second. the string snaps, find the further time taken for the 15 kg mass to return to its original position on the plane. Take g = 10 m//s^(2)

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Knowledge Check

  • Two masses M and m(M gt m) are joined by a light string passing over a smooth light pulley.

    A
    The acceleration of each block is `((M-m)/(M+m))g`
    B
    The tension in the string is `(2Mmg)/(M+m)`
    C
    The centre of mass of the 'M plus m' system moves down with an acceleration of `g((M-m)/(M+m))^(2)`
    D
    The tension in the string by which the pulley is attached to the rodd is `(M +m)g`

  • Two masses m and M(m lt M) are joined by a light string passing over a smooth and light pulley (as shown)

    A
    the acceleration of each mass is `((M-m)/(M+m))g`
    B
    the tension in the string connecting masses is `((2Mm)/(M+m))g`
    C
    the thrust acting on the pulley is `((4Mm)/(M+m))g`
    D
    None of the above

  • Two masses m_(1) and m_(2) are connected by light inextensible string passing over a smooth pulley P . If the pulley moves vertically upwards with an acceleration equal to g then .

    A
    Tension on the string is `(4m_(1)m_(2)g)/(m_(1)+m_(2))`
    B
    Tension on the string is `(2m_(1)m_(2)g)/(m_(1)+m_(2))`
    C
    The acceleration of mass `m_(1)` with respect to ground is `(3m_(2)-m_(1))/(m_(1)+m_(2))g` .
    D
    The acceleration of mass `m_(1)` with respect to ground is `(2(m_(2)-m))/(m_(1)+m_(2))g`

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