An object is released from rest. The time it takes to fall through a distance h and the speed of the object,
An object is released from rest. The time it takes to fall through a distance h and the speed of the object as it falls through this distance are measured with a pendulum clock. The entire apparatus is taken on the moon and the experiment is repeated
(a) the measured times are same
(b) the measured speeds are same
(c) the actual times in the fall are equal
(d) the actual speeds are equal.
1 Answers
(a) the measured times are same
(b) the measured speeds are same
EXPLANATION:
The time of fall t = √(2h/g) and the final speed v=√(2gh). The time period of the pendulum clock T=2π√(l/g). If the acceleration due to the gravity at the moon is g' = g/6, the actual time of fall will be t' = √6.t, i.e. √6 time more than that on the earth. (c) is not true.
Similarly, the actual speed v' =v/√6, i.e. only 1/√6 th of v. (d) is not true. Now the time period of the pendulum clock will be T'=√6.T, i.e. it will run √6 time slower than on the earth. Therefore the √6 times longer time of fall will be measured exactly the same by the √6 times slower clock. So (a) is true.
Since the clock shows the same time taken to fall through the same height, the measured speed will also be the same. (b) is true.