U = 13m/s j
a = -2 m/s² j
velocity will be zero at t = 13/2 = 6.5s
We need to find distance travelled in 7th second.
It is equal to distance travelled in 7 seconds minus distance travelled in 6 seconds.
Since it is changing its direction at t=6.5s, displacement will be 0 if we find the displacement in the 7th second. To find the distance travelled, find the distance travelled from 6 to 6.5 second and 6.5s to 7 second. Both will be same as time is same. So find the displacement from 6 to 6.5s and multiply it with 2.
S = (ut+0.5at²)₆.₅ - (ut+0.5at²)₆
⇒ S = (13×6.5 + 0.5×(-2)×6.5²) - (13×6 + 0.5×(-2)×6²)
⇒ S = 13(6.5-6) - 0.5×2×(6.5²-6²)
⇒ S = 13×0.5 - 1×(42.25-36)
⇒S = 6.5 - 6.25
⇒ S = 0.25m
So distance travelled in 7th second = 2S = 2×0.25 = 0.5m
Initial charges = Q and 3Q
When they are connected by a wire, charge distribution will happen according to the potential of the spheres. Since both are identical spheres, charge will be equally divided between the two.
The charges on both spheres will be (Q+3Q)/2 = 2Q