JEE Main 2023 · Physics · Kinematics and Laws of Motion · hard

A small bob is attached to a light inextensible string of length 0.5 m and is given a horizontal speed of 6 m s^-1 at the lowest point of its…

Numerical answer

A small bob is attached to a light inextensible string of length

0.5\ \mathrm{m}

and is given a horizontal speed of

6\ \mathrm{m\,s^{-1}}

at the lowest point of its vertical circular path. When the string becomes horizontal for the first time on the rising side, it snaps. The maximum height reached by the bob above the lowest point of the circle (in cm) is (

g=10\ \mathrm{m\,s^{-2}}

)

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Answer: 180

First check that the string stays taut up to the horizontal position: tension there is

\dfrac{mv^2}{L}>0

. Energy conservation up to the level of the string's pivot (

0.5\ \mathrm{m}

up):

v^2=u^2-2gL=36-10=26\ \mathrm{m^2\,s^{-2}}

. At that point the velocity is vertical (tangent to the circle), so after the string snaps the bob rises freely a further

h=\dfrac{v^2}{2g}=\dfrac{26}{20}=1.3\ \mathrm{m}

. Maximum height above the lowest point

=0.5+1.3=1.8\ \mathrm{m}=180\ \mathrm{cm}

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