Question

If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is(a) 2.5 m(b) 1 m(c) 1.5 m(d) 2 m

Answer 1

Answer:

2m

Explanation:

Length of rod = 3m

Distance between rods = x

Thus, p = kx where k is the constant mass of small element of dx length will be = dm = kx.dx

xcm = ∫x.dm/∫dm =∫x(xdx)/∫x.dx

= (x³/3)³/(x²/2)³\

= (27/3)/(9/2)

= 2

Thus, the distance of centre of gravity of the rod from end is 2m