SATHEE: Rotation 5 Question 11

Rotation 5 Question 11

21. Consider a body of mass $1.0 k g$ at rest at the origin at time $t = 0$ . A force $F = (α t \hat{i} + β \hat{j})$ is applied on the body, where $α = 1.0 N s^{- 1}$ and $β = 1.0 N$ . The torque acting on the body about the origin at time $t = 1.0 s$ is $τ$ Which of the following statements is (are) true?

(2108 Adv.) (a) $| τ | = \frac{1}{3} N - m$

(b) The torque $τ$ is in the direction of the unit vector $+ \hat{k}$

(d) The magnitude of displacement of the body at $t = 1 s$ is $\frac{1}{6} m$

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Answer:

Correct Answer: 21. (a,c)

Solution:

$F = (α t) \hat{i} + β \hat{j}$

$[at t = 0, v = 0, r = 0]$

$α = 1, β = 1 \Rightarrow F = t \hat{i} + \hat{j}$

$m \frac{d v}{d t} = t \hat{i} + \hat{j}$

On integrating,

$\begin{aligned} m v = \frac{t^{2}}{2} \hat{i} + \hat{t} [m = 1 k g] \\ \frac{d r}{d t} = \frac{t^{2}}{2} \hat{i} + \hat{t} = v \Rightarrow v = \frac{1}{2} (\hat{i} + 2 \hat{j}) at t = 1 s \end{aligned}$

Again, on integrating,

$r = \frac{t^{3}}{6} \hat{i} + \frac{t^{2}}{2} \hat{j} [r = 0 at t = 0]$

At $t = 1 s, τ = (r \times F) = \frac{1}{6} \hat{i} + \frac{1}{2} \hat{j} \times (\hat{i} + \hat{j}) = - \frac{1}{3} \hat{k}$

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Rotation 5 Question 11

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Rotation 5 Question 11

21. Consider a body of mass 1.0kg at rest at the origin at time t=0. A force F=(αti^+βj^) is applied on the body, where α=1.0Ns−1 and β=1.0N. The torque acting on the body about the origin at time t=1.0s is τ Which of the following statements is (are) true?

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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