The period of oscillation of an object in a frictionlesstunnel running through t

Question

The period of oscillation of an object in a frictionlesstunnel running through the Earth is 84.3 min. What is the period ofoscillation of an object in a similar tunnel on the Moon? (RE= 6.37 x 106 m; RM=1.74 x106m; ME = 5.98 x 1024kg; MM = 7.36 x 1022 kg) A.) 108.5 min B.) 143.3 min C.) 0.777 min
D.) 91.1 min E.) 4.61 x 10-3 min The period of oscillation of an object in a frictionlesstunnel running through the Earth is 84.3 min. What is the period ofoscillation of an object in a similar tunnel on the Moon? (RE= 6.37 x 106 m; RM=1.74 x106m; ME = 5.98 x 1024kg; MM = 7.36 x 1022 kg) A.) 108.5 min B.) 143.3 min C.) 0.777 min
D.) 91.1 min E.) 4.61 x 10-3 min

Explanation / Answer

The period of oscillation of an object in a frictionlesstunnel running through the Earth is 84.3 min. What is the period ofoscillation of an object in a similar tunnel on the Moon? (RE= 6.37 x 106 m; RM=1.74 x106m; ME = 5.98 x 1024kg; MM = 7.36 x 1022 kg) A.) 108.5 min B.) 143.3 min C.) 0.777 min
D.) 91.1 min E.) 4.61 x 10-3 min
T=2R/g
on earth
Te=2Re/ge
on moon
Tm=2Rm/gm
Tm/Te=Rm/Re*ge/gm=0.5226*2.449=1.2801
hence Tm=1.2801*84.3=107.91min=108min
hence option A is correct.

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