A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad s-2 The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

Question

A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad s-2 The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip) (A) 20 sec (B) 10 sec (C) 1.5 sec (D) 15 sec

Tardigrade Admin · Accepted Answer

At any instant linear acceleration of all points of coupled belt is same. a = r α r1 α1 = r2 α2 find α2 ω2 = ω1 + α2 t t = (ω2/α2) ∵ ω1 = 0

Q. A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad $s^{- 2}$ The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

20 sec

10 sec

1.5 sec

15 sec

At any instant linear acceleration of all points of coupled belt is same.
$a = r α$
$r_{1} α_{1} = r_{2} α_{2}$ find $α_{2}$
$ω_{2} = ω_{1} + α_{2} t$
$t = \frac{ω _{2}}{α _{2}}$ $∵ ω_{1} = 0$

Q. A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad s−2 The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)