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A bead B of mass 'm' can travel without ...

A bead `B` of mass `'m'` can travel without frictionn on a smooth horizontalwire `"xx"^(')`. The bead is connected to a block of identical mass by an ideal string passing over an ideal pulley. The system, as shown, is in vertical plane.

The system is allowed to fall. Find the speed of block `A` at the instant when string connected to the bead `B` makes an angle `37^(@)` with vertical.

A

`sqrt(ag)`

B

`sqrt((5ag)/17)`

C

`sqrt((27ag)/68)`

D

`sqrt((ag)/2)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Height dropped by `A`
`h=a/(cos60^(@))-a/(cos 37^(@))=(3a)/4`
`mgh=1/2 mv_(A)^(2)+1/2 mv_(B)^(2)`
Also, `v_(B)sin 37^(@)=v_(A)`
`implies (3ag)/4=(v_(A)^(2))/2[1+(5/2)^(2)]`
`=v_(A)=3/2 sqrt((3ag)/17)`
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