Let P(r) = Qr/πR4 be the charge density distribution for a solid sphere of radius R and total charge Q. for a point ‘p’ inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is
0
C.
A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as, where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of xCM on n?
A.
A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is
A.
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc.The value of α is
1/3
1/2
1/6
1/6
A.
1/3
In this question distance of centre of mass of new disc is αR not α/R.