Calculation of Potential Energy:

Since the body is ascending, its kinetic energy will be converted into potential energy.

Initial kinetic energy of the body = (1/2)mv^2 = (1/2) x 3 x (10)^2 = 150 J

Energy lost due to friction = 105 J

Therefore, final kinetic energy of the body = 150 - 105 = 45 J

Change in potential energy = mgh

where m = mass of the body = 3 kg

g = acceleration due to gravity = 10 m/s^2

h = height to which the body rises

Therefore, 45 = 3 x 10 x h

h = 1.5 m

However, this is not the final answer. This is because the height calculated above is the height the body would have risen if there was no energy lost due to friction. Since there was energy lost due to friction, the actual height to which the body will rise will be less than 1.5 m.

Calculation of Actual Height:

Let the actual height to which the body rises be H.

Total work done on the body = change in kinetic energy + change in potential energy + work done against friction

Since the body is starting from rest, its initial kinetic energy is zero.

Therefore, total work done on the body = change in potential energy + work done against friction

Total work done on the body = mgh + 105 J

Total work done on the body = 3 x 10 x H + 105

Total work done on the body = 30H + 105

Total work done on the body = final kinetic energy of the body = 45 J

Therefore, 30H + 105 = 45

30H = -60

H = -2 m

This answer is negative, which means that the body actually does not rise to a height of 2 m. This is because the negative sign indicates that the body actually descends instead of ascending.

Therefore, the correct answer is:

Actual height to which the body rises = 1.5 m - 2 m (due to energy lost due to friction)

Actual height to which the body rises = -0.5 m

However, since the question only asks for the height to which the body rises (and not the height to which it descends), we take the absolute value of the answer.

Therefore, the final answer is:

Actual height to which the body rises = | -0.5 | = 0.5 m

Hence, the correct option is 1. 0.5m.