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A rigid massless beam is balanced by a p...

A rigid massless beam is balanced by a particle of mass `4m` in left hand side and a pulley particle system in right hand side. The value of `x/y` is

A

`7/6`

B

`5/6`

C

`1:1`

D

`11//12`

Text Solution

Verified by Experts

The correct Answer is:
D
`a=((2m-m)g)/(3m)=g/3` for `T` in lower string,
`T=2mg-2mxxg/3=4 mg//3`
`& T^(1)=2T=(8mg)/3`
`T^(1)+mg=(8mg)/3+mg=(11mg)/3`
Let has take movent about hinge
`4mgxxx=(11 mg)/3xxyrArrx/y=11/12`
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Knowledge Check

  • A block of mass is connected to an ideal spring of stiffness K_(1) on left hand side and to an elastic strig of stiffness K_(2) on right hand side as shown in figure the time period of motion if mass m is displaced by 'x' as shown in figure.

    A
    `2pisqrt(m//K_(1))`
    B
    `2pisqrt(m//(K_(1)+K_(2)))`
    C
    `2pisqrt(m(K_(1)+K_(2))//K_(1)K_(2))`
    D
    `pi(sqrt((m)/(K_(1)+K_(2)))+sqrt((m)/(K_(1))))`

  • Two particle A and B, of mass m each, are joined by a rigid massless rod of length l. A particle P mass m, moving with a speed u normal to AB, strikes A and sticks to it. The centre of mass of the 'A+B+P' system is C.

    A
    The velocity of C before impact is u/3.
    B
    The velocity of C after impact is u/3
    C
    The velocity of 'A+P' immediately after impact is u/2.
    D
    The velocity of B immediately after impact is zero.

  • Three particles each of mass m are placed at the three corners of an equilateral triangle of side L. A particle of mass M is kept at the midpoint of any one side. What is the force acting on M, due to this system of 3 particles ?

    A
    `(GMm)/(4L^(2))`
    B
    `(3)/(4)(GMm)/(L^(2))`
    C
    `(4)/(3)(GMm)/(L^(2))`
    D
    `(4GMm)/(L^(2))`
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