MHT CET20255 May 2025Evening ShiftPhysicsWork, Power and EnergyActual
A stone of mass ' m ' kg is tied to a string of length ' L ' m and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take ^2=10 and acceleration due to gravity, g=10 ~m / s ^2 ]
Options
- A(90 ~m ) N
- B(60 ~m ) N
- C(45 ~m ) N
- D(15 ~m ) N
Correct answer
D. (15 ~m ) N
Step-by-step solution
The mass is m kg, with string length (radius) L = 0.49 m , and rotational frequency f = 0.5 rps . Angular velocity is = 2 f = rad/s . Centripetal acceleration becomes a_c = ^2 L = ( )^2 (0.49) = 10 0.49 = 4.9 m/s ^2 . At the lowermost point, the net centripetal force satisfies T - mg = ma_c . Solving yields the tension: T = m(g + a_c) = m(10 + 4.9) = 14.9m N . This gives T 15m N , corresponding to option D .