SATHEE: System of Particles and Rotational Motion - Result Question 25

System of Particles and Rotational Motion - Result Question 25

25. An automobile moves on a road with a speed of 54 $k m h^{- 1}$ . The radius of its wheels is $0.45 m$ and the moment of inertia of the wheel about its axis of rotation is $3 k g m^{2}$ . If the vehicle is brought to rest in $15 s$ , the magnitude of average torque transmitted by its brakes to the wheel is:

[2015 RS]

(a) $8.58 k g m^{2} s^{- 2}$

(c) $2.86 k g m^{2} s^{- 2}$

(b) $10.86 k g m^{2} s^{- 2}$

(d) $6.66 k g m^{2} s^{- 2}$

Show Answer

Answer:

Correct Answer: 25. (d)

Solution:

(d) Given : Speed $v = 54 k m h^{- 1} = 15 m s^{- 1}$

Moment of inertia, $I = 3 k g m^{2}$

Time $t = 15 s$

$ω_{i} = \frac{v}{r} = \frac{15}{0.45} = \frac{100}{3}$

[Given $ω_{f} = 0$ ]

$ω_{f} = ω_{i} + α t$

$0 = \frac{100}{3} + (- α) (15) \Rightarrow α = \frac{100}{45}$

Average torque transmitted by brakes to the wheel,

$τ = (I) (α) = 3 \times \frac{100}{45} = 6.66 k g m^{2} s^{- 2}$

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