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Chapter 2: Problem 272

Linear momentum of a particle is $(3 \mathrm{i} \wedge+2 \mathrm{j} \wedge-\mathrm{k} \wedge) \mathrm{kg} \mathrm{ms}^{-1}$. Find its magnitude. (A) \(\sqrt{14}\) (B) \(\sqrt{12}\) (C) \(\sqrt{15}\) (D) \(\sqrt{11}\)

Short Answer

Expert verified
The magnitude of the linear momentum is \(\sqrt{14}\) kg ms\(^{-1}\), which corresponds to option (A).

Step by step solution

01

Identify the components of the vector

The given linear momentum vector is \((3 \mathrm{i} \wedge+2 \mathrm{j}\wedge-\mathrm{k} \wedge) \mathrm{kg} \mathrm{ms}^{-1}\). Its components are: - \(x\)-component: \(3 \,\mathrm{kg} \, \mathrm{ms}^{-1}\) - \(y\)-component: \(2 \,\mathrm{kg} \, \mathrm{ms}^{-1}\) - \(z\)-component: \(-1 \,\mathrm{kg} \, \mathrm{ms}^{-1}\)
02

Calculate the sum of the squares of the components

Square each component and add them together: \(3^2 + 2^2 + (-1)^2 = 9 + 4 + 1 = 14\)
03

Find the square root of the sum

Take the square root of the sum to find the magnitude: \(\sqrt{14}\) The magnitude of the linear momentum is \(\sqrt{14}\) kg ms\(^{-1}\), which corresponds to option (A).

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Most popular questions from this chapter

A goods train is moving with constant acceleration. When engine passes through a signal its speed is U. Midpoint of the train passes the signal with speed \(\mathrm{V}\). What will be the speed of the last wagon? (B) \(\left.\sqrt{[}\left(\mathrm{V}^{2}-\mathrm{U}^{2}\right) / 2\right]\) (D) \(\sqrt{[}\left(2 \mathrm{~V}^{2}-\mathrm{U}^{2}\right)\)

Comprehensions type questions. A particle is moving in a circle of radius \(R\) with constant speed. The time period of the particle is T Now after time \(\mathrm{t}=(\mathrm{T} / 6)\) Average velocity of the particle is (A) \((3 \mathrm{R} / \mathrm{T})\) (B) \((6 \mathrm{R} / \mathrm{T})\) (C) \((2 \mathrm{R} / \mathrm{T})\) (D) \((4 \mathrm{R} / \mathrm{T})\)

A particle is thrown in upward direction with initial velocity of $60 \mathrm{~m} / \mathrm{s}$. Find average speed and average velocity after 10 seconds. \(\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]\) (A) \(26 \mathrm{~ms}^{-1}, 16 \mathrm{~ms}^{-1}\) (B) \(26 \mathrm{~ms}^{-1}, 10 \mathrm{~ms}^{-1}\) (C) \(20 \mathrm{~ms}^{-1}, 10 \mathrm{~ms}^{-1}\) (D) \(15 \mathrm{~ms}^{-1}, 25 \mathrm{~ms}^{-1}\)

Which from the following is true? (A) $\cos \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) / \mathrm{AB}\right]$ (B) $\sin \theta=\left[\left(\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}\right) / \mathrm{AB}\right]$ (C) $\tan \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) /\left(\mathrm{A}^{-}-\mathrm{B}^{-}\right)\right]$ (D) $\cot \theta=\left[\mathrm{AB} /\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right)\right]$

\(\mathrm{P}^{\rightarrow}=\mathrm{Q}^{\rightarrow}\) is true, if \(\ldots\) (A) their magnitudes are equal (B) they are in same direction (C) their magnitudes are equal and they are in same direction (D) their magnitudes are not equal and they are not in same direction
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