A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth?

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Answer 1 · 2016-06-13T18:43:24

#T_m~=0.75" "s#

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#T_e=2pi sqrt(l/g_e)" period equation for earth"#

#T_m=2pi sqrt(l/g_m)" period equation for mars"#

#(T_e)/(T_m)=(cancel(2pi) sqrt(l/g_e))/(cancel(2pi) sqrt(l/g_m))#

#" plug "T_e=0.80 s#

#(0.80)/(T_m)=sqrt((l/(g_e))/(l/(g_m)))" #

# (0.80)/(T_m)=sqrt(cancel(l)/(g_e)*(g_m)/cancel(l)#

#(0.80)/T_m=sqrt((g_m)/(g_e))#

#" plug " g_e=g" "g_m=0.37g#

#(0.80)/(T_m)=sqrt((0.37*cancel(g))/cancel(g))#

#(0.80)/T_m=sqrt(0.37)#

#((0.80)/T_m)^2=(sqrt(0.37))^2#

#(0.64)/T_m^2=0.37#

#T_m^2=(0.37)/(0.64)#

#T_m=sqrt((0.37)/(0.64))#

#T_m~=(0.6)/(0.8)#

#T_m~=6/8=3/4#

#T_m~=0.75" "s#