Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

  • 0.02

  • 0.03

  • 0.04

  • 0.04


A.

0.02

According to law of tension, the frequency of the string varies directly as the square root of its tension


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A mass m moving horizontally (along the x -axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y -axis) with velocity 2v. The final velocity of the combination

  • 1 half straight v space bold i with bold hat on top space plus 3 over 2 straight v space bold j with bold hat on top
  • 1 third straight v space bold i with bold hat on top space plus 2 over 3 straight v space bold j with bold hat on top
  • 2 over 3 straight v space bold i with bold hat on top space plus 1 third straight v space bold j with bold hat on top
  • 2 over 3 straight v space bold i with bold hat on top space plus 1 third straight v space bold j with bold hat on top

A.

1 half straight v space bold i with bold hat on top space plus 3 over 2 straight v space bold j with bold hat on top

From the law of conservation of linear momentum



mv + (3m)(2v) = (4m)v'

mv + 6mv j = 4 mv'


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Two stone of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

  • 2

  • 3

  • 4

  • 4


A.

2

Given, that two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and lighter one in radius r as shown in a figure.



As lighter stone is n times that of the value of heavier stone when they experience same centripetal forces, we get

(Fc)heavier = (Fc)lighter

2605 Views

A block of mass m is in contact with the cart C as shown in the figure

The coefficient of static friction between the block and the cart is μ. The acceleration α of the cart that will prevent the block from falling satisfies

  • straight alpha space greater than mg over straight mu
  • straight alpha space greater than space straight g over μm
  • straight alpha space greater or equal than space straight g over straight mu
  • straight alpha space greater or equal than space straight g over straight mu

C.

straight alpha space greater or equal than space straight g over straight mu

When a cart moves with some acceleration toward right then a pseudo force (mα) acts on block towards left. The force (mα) is action force by a block on the cart. Now, block will remain static w.r.t cart if frictional force 

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A ball moving with velocity 2 ms-1 collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms-1) after collision will be

  • 0,1

  • 1,1

  • 1,0.5

  • 1,0.5


A.

0,1

If two bodies collide head on with coefficient of restitution

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