Asimple pendulum is mounted in an elevator. what happens to the period of the pendulum (does it increase, decrease, or remain the same) if the elevator

(a) accelerates upward at 5.0 m/s2;
(b) moves upward at a steady 5.0 m/s ;
(c) accelerates downward at 5.0 m/s2;
(d) accelerates downward at 9.8 m/s2

Explanation:

Time period of Simple pendulum is given by

where L=length of Pendulum

g=acceleration due to gravity

(a)When elevator is accelerating upward with

effective g will be g+a=9.8+5

therefore time period will decrease

(b)When elevator is moving upward with 5 m/s

effective g will be g as there is no added acceleration

therefore time period will remain same

(c)When elevator is accelerating downward with

effective g will be g-a=9.8-5

therefore time period will increase

(d)When elevator is accelerating downward with

effective g will be g-9.8=0

therefore time period will become infinite

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft