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A solid ball is suspended from the ceili...

A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed `60 cm^(-1)`. The acceleration of the car is nearly `(g=10 ms^(-2))`

A

`4.3 ms^(-2)`

B

`2.9 ms^(-2)`

C

`6.8 ms^(-2)`

D

`5.5 ms^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
When car is at rest, tension in string is T= mg.
`T=Mg =mv_(1)^(2)`
`V_(1) =sqrt((T)/(r) =)sqrt((Mg)/(mu))" ...(i)"`

When car is accelerating tension.
`T=sqrt(M(a^(2)+g^(2))^(1//2))`
`therefore" "v_(2) =sqrt((M(a^(2)+g^(2))^(1//2))/(mu))`
Dividing Eq (i) by Eq. (ii), we get
`(v_(2))/(v_(1))=sqrt((M(a^(2)+g^(2))^(1//2))/(sqrt(Mg)))=(66)/(60)`
`((a^(2)+g^(2))^(1//2))/(g) =(121)/(100)`
Squaring, we get
`rArr a^(2)+g^(2) =((121)/(100))^(2)`
`rArr a^(2)=146.41-100`
`rArr a^(2)=46.41`
So, `a=6.8 ms^(-2)`
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