To determine the temperature at a point 50 cm from the hotter end of the bar, we can use the formula for linear temperature distribution in a bar:
T = (90 - 30) * (x/10) + 30
where T is the temperature at a point x cm from the hotter end, 90°C is the temperature at the hotter end, 30°C is the temperature at the cooler end, and 10 cm is the length of the bar.
Substituting 50 cm for x in the formula above, we get:
T = (90 - 30) * (50/10) + 30
= 60 * 5 + 30
= 300 + 30
= 330
Therefore, the temperature at a point 50 cm from the hotter end of the bar is 330°C.