Physics

System of Particles and Rotational Motion

Torque

Consider a body of mass 1.0 {~kg} at rest at the origin at tim

Question

Hard

Solving time: 4 mins

Consider a body of mass $1.0 kg$ 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 $α = 1.0 Ns^{- 1}$ 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?

Name: Video answer for Consider a body of mass 1.0 kg 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=1.0 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?
Uploaded: 2022-08-20T03:19:35.000Z
Duration: 12 min
Description: Consider a body of mass 1.0 kg 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=1.0 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?

SELECT MULTIPLE OPTION

∣ τ ∣ = \frac{1}{3} N - m

The torque

τ

is in the direction of the unit vector

+ \hat{k}

The velocity of the body at

t = 1 s

v = \frac{1}{2} (\hat{i} + 2 \hat{j}) ms^{- 1}

The magnitude of displacement of the body at

t = 1 s

\frac{1}{6} m

Views: 5,839 students

Updated on: Aug 20, 2022

Book:

Mechanics Volume 2 (DC Pandey)

Text solutionVerified

F = (α t) \hat{i} + β \hat{j} [at t = 0, v = 0, r = 0]

α = 1, β = 1

F = t \hat{i} + \hat{j}

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

On integrating, m v = \frac{t ^{2}}{2} \hat{i} + t \hat{j} [m = 1 kg]

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

Again, on integrating,

r = \frac{t ^{3}}{6} \hat{i} + \frac{t ^{2}}{2} \hat{j}

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

τ = \frac{1}{3} \hat{k}

v = \frac{t ^{3}}{2} \hat{i} + t j

t = 1 s, v = (\frac{1}{2} \hat{i} + \hat{j}) = \frac{1}{2} (\hat{i} + 2 \hat{j}) m / s

t = 1 s, r_{1} - r_{0} = [\frac{1}{6} \hat{i} + \frac{1}{2} \hat{j}] - [0]

s = \frac{1}{6} \hat{i} + \frac{1}{2} \hat{j}

∣ s ∣ = (\frac{1}{6})^{2} + (\frac{1}{2})^{2} \Rightarrow \frac{10}{6} m

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Theodore Discussed

Consider a body of mass

1.0 kg

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 Ns^{- 1}

and

β = 1.0 N

. The torque acting on the body about the origin at time

t = 1.0 s

τ

. Which of the following statements is (are) true?

13 mins ago

Discuss this question LIVE

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Question Text	Consider a body of mass $1.0 kg$ 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 $α = 1.0 Ns^{- 1}$ 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?
Updated On	Aug 20, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	204
Avg. Video Duration	12 min

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Consider a body of mass 1.0 kg 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=1.0 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?

Text solutionVerified

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