Question

A stone of mass 1 kg tied to a light string of length ( = 10 m is whirling in a circular path in the vertical
plane. If the ratio of the maximum to minimum tensions in the string is 3, find the speeds of the stone at
the lowest and highest points,
where T2-T1 =3 is given ​

Answer 1

Explanation:

Correct option is

D

10ms

−1

Given,

suppose:max.tension(T

1

)andmim.tension(T

2

).

T

2

T

1

=4

T

1

=4T

2

Nowasdiffbetweenmax.tensionandmim.tensionforabodyinvertical

circleis:

T

1

−T

2

=6mg

4T

2

−T

2

=6mg

3T

2

=6mg

T

2

=2mg

Now,

Higestpointmin.tensioncanbe:

T

2

=

r

mv

2

−mg

2mg=

r

mv

2

−mg

3mg=

r

mv

2

∴v=

3gr

Here,r=L=

3

10

v=

3×10×

3

10

v=

100

m/s

∴10ms

−1

sothatthecorrectoptionisD.

Answer 2

Explanation:

TheratiotothemamimumT

2

totheminimumtensionT

1

is−

T

1

T

2

=4

T

2

=4T

1

Nowthedifferencebetweenthetwo6mg;

Hencewehave

T

2

−T

1

=6mg

∴4T

1

−T

1

=6mg

3T

1

=6mg

T

1

=2mg

Nowtensionatthetopofthecircleis−

T

1+mg

=

r

mv

1

2

=

L

mv

1

2

2mg+mg=

3

10

mv

1

2

v

1

2

=3g

3

10

=10g

v

1

=

10g

=

10×10

=10m/s