Show that the centre of a rod of mass m and length l lies midway between the ends assuming that the rod has uniform cross section per unit length

Explanation:

The cross section per unit length is uniform, so ρ is constant.

The center of mass is therefore:

x_avg = (∫₀ᴸ x ρ dL) / (∫₀ᴸ ρ dL)

x_avg = (∫₀ᴸ x dL) / (∫₀ᴸ dL)

x_avg = (½ L²) / (L)

x_avg = ½ L

it becomes positively charged by charging it

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s