physics problems (5)

Question

10. a ball of a mass m at the end of a string is swung in a horizontal circular path if radius R at constant speed V. which combination of changed would require the greatest increase in the centripetal force acting on the ball ?(1) 2V and 2R (2) 2V and 1/2R (3) 0.5R and 2V(4) 0.5V and 0.5V

11. an airplane is moving with a constant velovity in level flight. compare the magnitude of the forward force provided by the engines to the magnitude of the backward frictional drag force.

Explain!

Answer 1

10. Since centripetal force F=mV^2/R (where m is the mass of the ball)
Any increase in V or decrease of R will make F to increase.
therefore, look for the option with the greatest increase in V and greatest decrease in R.
The answer should be option (2)
Note: you migth have typed wrongly the answers in options (3) and (4). Option (3) and (2) seems the same; and option (4) has no R.
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11. Since the plane is at constant speed, the net force acting on it is zero. Hence, the forward force should be equal to the backward drag force.