অভিকর্ষ ও অভিকর্ষজ ত্বরণ

A body weighs 900900N on the earth. Find its weight on a planet whose density is 13st\dfrac{1}{3}^{st} the density of earth and radius is 14th\dfrac{1}{4}^{th} that of the earth.

হানি নাটস

Weight of object on earth W=GMmR2W = {\dfrac{GMm}{R^2}}

Now, M=ρVM = {\rho}V =4πρR33{\dfrac{4\pi \rho R^{3}}{3}}

W=GρπR3Gm3R2=4πρRGm3\therefore W = {\dfrac{G \rho \pi R^{3} G m}{3 R^{2}}} = {\dfrac{4 \pi \rho R G m}{3}}

WPWE=(ρPρE)(RPRE){\dfrac{W_P}{W_E}} = {(\dfrac{\rho_P}{\rho_E})}{(\dfrac{R_P}{R_E})}

=13×14 = {\dfrac{1}{3}} \times {\dfrac{1}{4}} = 112{\dfrac{1}{12}}
WP=90012=75N{W_P} = {\dfrac{900}{12}} = 75 N

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