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5.Work, Energy, Power and Collision
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$m$ संहति के पत्थर को किसी डोरी के एक सिरे से बाँधकर $R$ त्रिज्या के ऊध्वाधर वृत्त में घुमाया जाता है। वृत्त के निम्नतम तथा उच्चतम बिंदुओं पर ऊध्वाधरत: अधोमुखी दिशा में नेट बल हैं : (सही विकल्प चुनिए)
| निम्नतम बिंद पर | उच्चतम बिंदु पर |
| $(i)$ ${mg - {T_1}}$ | ${mg + {T_2}}$ |
| $(ii)$ ${{m_g} + {T_1}}$ | ${{m_g} - {T_2}}$ |
| $(iii)$ ${mg + {T_1} - \frac{{mv_1^2}}{R}}$ | ${mg - {T_2} + \frac{{mv_1^2}}{R}}$ |
| $(iv)$ ${mg - {T_1} - \frac{{mv_1^2}}{P}}$ | ${mg + {T_2} + \frac{{mv_1^2}}{p}}$ |
Option A
Option B
Option C
Option D
Solution
The free body diagram of the stone at the lowest point is shown in the following figure.According to Newton’s second law of motion, the net force acting on the stone at this point is equal to the centripetal force, i.e.,
$F_{net}=T-m g=\frac{m v_{1}^{2}}{R}$
Where, $v_{1}=$ Velocity at the lowest point
The free body diagram of the stone at the highest point is shown in the following figure.
Using Newton's second law of motion, we have:
$T+m g=\frac{m v_{2}^{2}}{R}$
Where, $v_{2}=$ Velocity at the highest point It is clear from above equations that the net force acting at the lowest and the highest points are respectively $(T-m g )$ and $(T+m g )$
Standard 11
Physics
