Question

a pendulum bob is given velocity u = root(7gr/2) at lowest point where r is length of the string then the minimum velocity of bob in subsequent motion is

Answer 1

Answer:

Lets A is the topmost point of the circle and B be the lowest point of the circle.

Let v

2

and v

1

be the velocities at B and A respectively.

Applying the principle of conservation of energy between A and B.

2

1

mv

2

2

−

2

1

mv

1

2

=mg2l

or

l

mv

2

2

=

l

mv

1

2

+4mg .....(1)

At B,

l

mv

2

2

=T−mg .....(2)

At A.

l

mv

1

2

=mg ....(3)

Solving (1), (2) and (3)

or mg+4mg=T−mg or T=6mg