Question

A wheel with radius $45$cm rolls without slipping along a horizontal floor as shown in figure. P is a dot pointed on the rim of the wheel. At time $t_1$, P is at the point of contact between the wheel and the floor. At a later time $t_2$, the wheel has rolled, through one-half of a revolution. What is the displacement of P during this interval.

• A. $90$cm
• B. $168$cm
• C. $40$cm
• D. Data insufficient

Answer 1

The correct option is B $168$cm

Let d be the displacement

now x = $\pi \ast r=45\ast \pi =141.37cm$ = horizontal displacement

y= 2r = 90 cm =vertical displacement

$d=\sqrt{x^2+y^2}=168cm$