Question

The Palomar telescope’s 5-m mirror weighs 14.5 tons. If a 10-m mirror were constructed of the same thickness as Palomar’s (only bigger), how much would it weigh?

Answer 1

58 tons

Step-by-step explanation:

Diameter of Palomar telescope mirror = 5 m

Radius of Palomar telescope mirror = 2.5 m

h = Thickness of mirror

Volume of mirror of 5 m diameter = πr²h = π2.5²h

Volume of mirror of 10 m diameter = π5²h

Mass of second mirror

Assuming the material of the mirrors are same the density will be same.

`\rho=(mass)/(volume)`

`\\\Rightarrow (14.5)/(\pi 2.5^2h)=(m)/(\pi 5^2h)\\\Rightarrow (14.5)/(2.5^2)=(m)/(5^2)\\\Rightarrow m=(14.5)/(2.5^2)* 5^2\\\Rightarrow m=58\ tons`

∴ Weight of the mirror if it were 10 m diameter is 58 tons