Question

A parabolic bowl with its bottom at origin has the shape y = x²/20. Here x and y are in metres, the maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5) is-

• A. 2.5 m
• B. 1.25 m
• C. 1.0 m
• D. 4.0 m

Answer 1

Answer: (B)

1.25 m

Answer 2

For the equation µN = mg sin q

Ž µmg cos q = mg sin q Ž tan q = µ = $\frac { 1 } { 2 }$ ...(i)

From equation y = $\frac { x ^ { 2 } } { 20 }$

Ž tan q = $\frac { d y } { d x }$ = $\frac { x } { 10 }$ .... (ii)

From (i) & (ii) , x = 5 , so y = 1.25