Question

Auniform cylindrical container is half filled with water. The height of the cylinder is it is twice its diameter.The cylinder is gradually tilted until the water touches the brim. At this instant the container is inclined at
1)30° to vertical
2)45°to vertical
3)60° to vertical
4)75° to vertical

Answer 1

It is given that height of the cylinder is twice that of its diameter.

Meaning if height = h, the diameter will be h / 2

Using this we can imagine that when we tilt the cylinder until the water touches the brim.

The height falls to half of its original height since the it was initially half filled.

Using formula

Sin x(angle of tilt) = D / h

D = 1/2h

Sin x = 1/2 ÷ 1 = 1/2

We get, sin x = 1/2

Sin⁻¹ 0.5 = 30°

x = 30 degrees

option A is correct
thank u