question_answer

As shown in fig. when a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e. on the surface of the cavity. R can be determined by the equation                                    [JEE MAIN Held on 08-01-2020 Evening]

A)   \[\left( {{R}^{2}}\text{+}R+1 \right)\left( 2R \right)=1\]

B)   

C)   

D)   

Correct Answer: A

Solution :

[a]               \[{{M}_{0}}=\frac{4}{3}\pi {{R}^{3}}\rho \]               x