A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. Then the magnitude of gravitational force exerted by earth on the rod is :
A
GMm4R2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
GMm2R2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4GMm9R2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
GMm8R2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is BGMm2R2 Consider an element of length dx and mass dm
Here, dm=(mRdx)
Force on element dx of the rod is dF=(mRdx)GMx2
Total force on rod is F=∫dF=GMmR2R∫R1x2dx =GMmR[−1x]2RR =GMm2R2