Question

Two wheels having radii in the radio 1:3 are con-
nected by a common belt. If the smaller wheel is
accelerated from rest at a rate 1.5rad s-2 for 10
s. Find the angular velocity of bigger wheel.
(1) 5 rad s-1
(2) 15 rad s-1
(3) 45 rad s-1
(4) 60 rad s-1​

Answer 1

Answer:

The angular velocity of bigger wheel is 5 rad/sec

Explanation:

Given as :

The radius of two wheel = 1 : 3

radius of smaller wheel = x

Radius of larger wheel = 3 x

Wheels are connected to common belt

The acceleration rate of smaller wheel = $\omega$ = 1.5 rad/s²

Time period of acceleration = t = 10 sec

Let The angular velocity of bigger wheel =  $\omega_2$  rad/sec

According to question

From standard equation

$\omega$ = $\omega_0$  + $\omega$ t

i.e $\omega$ = 0 + 1.5 × 10

i.e $\omega$ = 15 rad/ sec

Again

∵ wheels are connected to common belt then there linear velocity is constant

i.e  $v_1 = v_2$

Or, $r_1 \omega _1$  = $r_2 \omega _2$

Or, r ×  15 rad/sec  = 3 r × $\omega_2$

or, 15 =  3  × $\omega_2$

∴    $\omega_2$  = $\dfrac{15}{3}$

i,e   $\omega_2$  = 5 rad/sec

Hence, The angular velocity of bigger wheel is 5 rad/sec  . Answer

 

Answer 2

Answer:

5 rad s-1

Explanation:

smaller = x

bigger = 3x

Smaller wheel = 1.5 rad/sec

Bigger wheel = w2

w= w0+wt

= 0+1.5×10=15 rad/sec

v1= v2

r1w1=r2w2

r×15=,3r×w2

15= 3×w2

w2 =5 rad s-1

The Answer is option no [1]