Answer:
Explanation:
Given
mass of first sphere is M and radius R
Mass of other sphere is 8 M and radius 2 R
acceleration of a rolling body in an inclined plane is given by
[tex]a=\frac{g\sin \theta }{1+\frac{I}{mR^2}}[/tex]
where I=moment of Inertia
m=mass of object
R=radius of object
[tex]\theta [/tex]=inclination of plane
Moment of inertia of first body [tex]I=\frac{2}{5}MR^2[/tex]
Moment of inertia other body [tex]I'=\frac{2}{5}(8M)(2R)^2=\frac{64}{5}MR^2[/tex]
acceleration of first body [tex]a_1=\frac{g\sin \theta }{1+\frac{\frac{2}{5}MR^2}{MR^2}}[/tex]
[tex]a_1=\frac{5}{7}g\sin \theta [/tex]
acceleration of second body [tex]a_2=\frac{g\sin \theta }{1+\frac{\frac{64}{5}MR^2}{8M(2R)^2}}[/tex]
[tex]a_2=\frac{g\sin \theta }{1+\frac{2}{5}}[/tex]
[tex]a_2=\frac{5}{7}g\sin \theta [/tex]
thus acceleration of first and second is same therefore they will reach at the same time
