A wheel is rotating about an axis through its centre at 720 rpm . It is acted on by a constant torque opposing its motion for text8 s to bring it to rest finally. The value of torque ( textin N m) is ( textGiven I = (24/π ) kg m2)

Question

A wheel is rotating about an axis through its centre at 720 rpm . It is acted on by a constant torque opposing its motion for text8 s to bring it to rest finally. The value of torque ( textin N m) is ( textGiven I = (24/π ) kg m2) (A) 48 (B) 72 (C) 96 (D) 120

Tardigrade Admin · Accepted Answer

In given question torque is constant
So

τ = \frac{L _{2} - L _{1}}{t _{2} - t _{1}}

... (i)

L

is angular momentum here
Given

t_{2} - t_{1} = 8 s, L_{1} = I ω_{1} an d L_{2} = 0

ω_{1} = 2 πn, h ere n = 720 r p m

So

n = \frac{720}{60} r p s = 12 r p s

(r p s = rotations per second)

So from eq

(i) τ = \frac{0 - ( \frac{24}{π} ) ( 2 π ( 12 ) )}{8}

τ = - 72 N m

So

τ = 72 N m

(Opposing Torque)

Q. A wheel is rotating about an axis through its centre at $720 r p m$ . It is acted on by a constant torque opposing its motion for $8 s$ to bring it to rest finally. The value of torque $(in N m)$ is $(Given I = \frac{24}{π} k g m^{2})$

$48$

$72$

$96$

$120$

Q. A wheel is rotating about an axis through its centre at 720rpm . It is acted on by a constant torque opposing its motion for 8 s to bring it to rest finally. The value of torque (inNm) is (GivenI=π24​kgm2)

48

72

96

120

Q. A wheel is rotating about an axis through its centre at $720 r p m$ . It is acted on by a constant torque opposing its motion for $8 s$ to bring it to rest finally. The value of torque $(in N m)$ is $(Given I = \frac{24}{π} k g m^{2})$

$48$

$72$

$96$

$120$