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 :

$x ^ { 2 }$

• 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

$\frac { d y } { d x }$ = $\frac { x } { 10 }$

or tan q = $\frac { x } { 10 }$ … (i)

Equilibrium of mass in horizontal direction gives the equation,

µN cos q = N sin q

or tan q = µ = $\frac { 1 } { 2 }$ … (ii)

From Eqs. (i) and (ii)

$\frac { x } { 10 }$ = $\frac { 1 } { 2 }$ or x = 5 m

\ y = $\frac { x ^ { 2 } } { 20 }$ = $\frac { 25 } { 20 }$ = 1.25 m