Question

8. If we drop four balls (same material, same density) with different size separately into the same glycerine, which one's terminal speed is the smallest? A. Ball with diameter 1m B. Ball with diameter 0.5m C. Ball with diameter 0.1m D. Ball with diameter 0.05m

Answer 1

ONE QUESTION AT A TIME PLEASE...............PLEASE FOLLOW THE RULES

------------------------------------------------------

8)

terminal speed is when drag force equals weight

1/2 * $\rho$ * v² * A * C_d = mg

v = sqrt ( 2mg / $\rho$ A C_d)

for the same shape and material, the terminal velocity of an object increases with size.

so,

ball with least size will have smallest terminal speed

option D looks fine

------------------------------------------------

6)

the moment of inertia of hollow cylinder is

I = 1/2 * m * (r² + R² )

where r and R are internal and external radii

so,

I = 1/2 * 8 ( 0.05² + 0.1²)

I = 0.05 kg.m² (this is the moment of inertia about central axis of cylinder)

to find moment of inertia about axis parallel to cylinder, we can use parallel axis theorem

I' = I + mx²

where x is the distance between outer axis and center of cylinder

I' = 0.05 + 8 * 1

I' = 8.05 Kg.m²

-----------------------------------------------