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Chapter 4: Problem 561

The velocity of a body of mass \(400 \mathrm{gm}\) is $(-3 \mathrm{i} \wedge-4 \mathrm{j} \wedge) \mathrm{m} / \mathrm{s}$. So its kinetic energy is ...... (A) \(5 \mathrm{~J}\) (B) \(10 \mathrm{~J}\) (C) \(8 \mathrm{~J}\) (D) \(16 \mathrm{~J}\)

Short Answer

Expert verified
The kinetic energy of the body is 10 Joules. The correct answer is (B) \(10 \mathrm{~J}\).

Step by step solution

01

Convert mass to kg

First, convert the mass of the body from grams to kilograms (since we need the mass in kg for the kinetic energy formula). Recall that 1 kg = 1000 gm. Mass, m = 400 gm = 400 / 1000 kg = 0.4 kg
02

Find the magnitude of the velocity vector

The velocity vector is given as (-3i - 4j) m/s. Find the magnitude of this vector given by: v = \( \sqrt{(-3)^2 + (-4)^2} \) Calculate within the square root: v = \( \sqrt{9 + 16} \) Now, the square root: v = \( \sqrt{25} \) = 5 m/s
03

Calculate the kinetic energy

Now that we have the mass in kg and the magnitude of the velocity in m/s, we can calculate the kinetic energy using the formula KE = (1/2) * m * v^2. KE = (1/2) * 0.4 kg * (5 m/s)^2 Calculate the square of the velocity: KE = (1/2) * 0.4 kg * 25 (m^2/s^2) Now multiply by mass and (1/2): KE = 10 J The kinetic energy of the body is 10 Joules. The correct answer is (B) \(10 \mathrm{~J}\).

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Most popular questions from this chapter

An ice-cream has a marked value of \(700 \mathrm{kcal}\). How many kilo-watt- hour of energy will it deliver to the body as it is digested $(\mathrm{J}=4.2 \mathrm{~J} / \mathrm{cal})$ (A) \(0.81 \mathrm{kwh}\) (B) \(0.90 \mathrm{kwh}\) (C) \(1.11 \mathrm{kwh}\) (D) \(0.71 \mathrm{kwh}\)

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one third of its is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on to the table is (A) MgL (B) \([(\mathrm{MgL}) /(3)]\) (C) \([(\mathrm{MgL}) /(9)]\) (D) \([(\mathrm{MgL}) /(18)]\)

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