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Dimensional Analysis

74.When a bob...

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74.When a bob is suspended by light string and it is imparted a horizontal velocity to complete the full circular trajectory in vertical plane. What is the difference in tension between lowest and highest point

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Q. A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity

v_{0}

at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C. This is shown in Fig. 6.6. Obtain an expression for (i)

v_{0}

; (ii) the speeds at points B and C; (iii) the ratio of the kinetic energies

(K_{B} / K_{C})

at B and C. Comment on the nature of the trajectory of the bob after it reaches the point C.

Q. A bob of mass

m

, suspended by a string of length

l_{1}

is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass

m

suspended by a string of length

l_{1}

, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio

l_{1} / l_{2}

Q. A bob of mass

m

, suspended by a string of length

l_{1}

, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass

m

suspended by a string of length

l_{2}

, which is initially at rest. Both the strings are massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio

\frac{l_{1}}{l_{2}}

Q. A simple pendulum is suspended from the fixed point and

m

is mass of bob. When the bob is at the lowest position, the bob is given a minimum velocity in horizontal direction so that the bob describes vertical circle. When the string is horizontal, the tension in it is:

Q. A bob attached to a light string is rotating in a vertical circle of radius

5 m

. If the velocity of the bob at its lowest point is twice the velocity of the bob when it makes an angle of

90^{0}

with the vertical. Will the bob complete a full circle? If yes, what is the velocity of the bob at its highest point?

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