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A 50-kg ball is attached to one end of a...

A `50-kg` ball is attached to one end of a `1m` cord that has a mass of `0.10kg`. The other end o the cord is attached to a ring that can slide on a frictionless horizontal shaft `AB`, as shown in the diagram.
A horizontal blow is delivered to the cord and excites the fundamental vibratiion with a maximum transverse velocity of `15m//s`. Assume that the ball remains essentially stationary as the cord vibrates. `[g=9.8m//s^(2)]`

A

The frequency of the fundamental vibration is `17.5Hz`

B

The amplitude of the motion is `13.6xx10^(-2)m`

C

If the blow is delivered as an impulse to a stationary cord, the wave function for the cord is `y(x,t)=Asin(pix//2L)sinomegat`, where the ball is located at `x=0` and positive `x`-axis is along the string.

D

The period of the pendulum motion of the hanging ball is 2 sec, approximately.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`v=sqrt(T/(mu))=sqrt((50xx1xx9.8)/0.1)=70m//s`
`(lamda)/4=1implieslamda=4mimpliesf=f/(lamda)=70/4=17.5Hz`
`v_("pmax")=omegaAimpliesA=(v_("pmax"))/(2pif)=15/(2xx3.14xx17.5)=0.136m=13.6xx10^(-2)m`
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