First slide

Toppling

Question

A heavy wheel of radius 20 cm and weight 10 kg is to be dragged over a step of height 10 cm, by a horizontal force F applied at the centre of the wheel. The minimum value of F is

Difficult

A

20 kgwt
B

1 kgwt
C

10√3 kgwt
D

10√2 kgwt

Solution

Height of step = 10 cm; OA = 20 cm; OB = 10 cm
Toppling moment about A must be greater than restoring moment about A.

$\large \therefore F\times OB>mg\times AB$

$\large \Rightarrow F\times 10>(10\times 10)\times \sqrt {20^2-10^2}$

$\large \Rightarrow F>100\sqrt 3N$

$\large \therefore F_{min}=10\sqrt 3kg-wt$

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