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.
Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
(5/6)ma2
(1/12)ma2
(7/12)ma2
(7/12)ma2
D.
(7/12)ma2
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.