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  4. A disc of radius 0.1 m rolls without sliding on a horizontal surface with a velocity of 6 ms- 1 . It then ascends a smooth continuous track as shown in figure. The height upto which it will ascend is (in cm ): ( g=10 m s- 2 ) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-zivh4lmtkaxvvfuk.jpg />

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Q. A disc of radius $0.1 \, m$ rolls without sliding on a horizontal surface with a velocity of $6 \, ms^{- 1}$ . It then ascends a smooth continuous track as shown in figure. The height upto which it will ascend is (in $cm$ ) : ( $g=10 \, m s^{- 2}$ )

Question

NTA AbhyasNTA Abhyas 2022

Solution:

Since it ascends on a smooth track it will not experience any torque. Therefore, its rotational kinetic energy will not change. Hence, only translational kinetic energy will convert into potential energy.
$\Rightarrow \frac{1}{2}mv^{2}=mgh \, $
$\Rightarrow h=\frac{v^{2}}{2 g}\Rightarrow h=\frac{6^{2}}{2 \times 10}=1.8\,m=180\,cm$