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Chapter 4: Problem 480

A bomb of mass \(10 \mathrm{~kg}\) explodes into 2 pieces of mass $4 \mathrm{~kg}\( and \)6 \mathrm{~kg}\(. The velocity of mass \)4 \mathrm{~kg}$ is \(1.5 \mathrm{~m} / \mathrm{s}\), the K.E. of mass \(6 \mathrm{~kg}\) is ....... (A) \(3.84 \mathrm{~J}\) (B) \(9.6 \mathrm{~J}\) (C) \(3.00 \mathrm{~J}\) (D) \(2.5 \mathrm{~J}\)

Short Answer

Expert verified
The kinetic energy of mass \(6\mathrm{~kg}\) is \(3.00 \mathrm{~J}\).

Step by step solution

01

Apply the Principle of Conservation of Linear Momentum

According to the Principle of Conservation of Linear Momentum, the total momentum before the explosion is equal to the total momentum after the explosion. In this case, the initial momentum of the bomb is zero, so the combined momentum of the two pieces after the explosion must also be zero.
02

Calculate the velocity of mass \(6\mathrm{~kg}\)

Let the velocity of the mass \(6\mathrm{~kg}\) be \(v\). The combined momentum of the two pieces after the explosion can be expressed as: \(4\mathrm{~kg} \cdot 1.5\mathrm{~m/s} = 6\mathrm{~kg} \cdot v\) Now, solve for \(v\): \(v = \dfrac{4\mathrm{~kg} \cdot 1.5\mathrm{~m/s}}{6\mathrm{~kg}}\) \(v = 1\mathrm{~m/s}\) So the velocity of the mass \(6\mathrm{~kg}\) is \(1\mathrm{~m/s}\).
03

Calculate the kinetic energy of mass \(6\mathrm{~kg}\)

Now that we have the velocity of mass \(6\mathrm{~kg}\), we can calculate its kinetic energy using the formula: \(KE = \dfrac{1}{2} m v^2\) where \(KE\) is the kinetic energy, \(m\) is the mass and \(v\) is the velocity. Substitute the given values: \(KE = \dfrac{1}{2} \cdot 6\mathrm{~kg} \cdot (1\mathrm{~m/s})^2\) \(KE = \dfrac{1}{2} \cdot 6\mathrm{~kg} \cdot 1\mathrm{~m^2/s^2}\) \(KE = 3\mathrm{~J}\) The kinetic energy of mass \(6\mathrm{~kg}\) is \(3\mathrm{~J}\).
04

Select the correct option

From our calculations, we have found that the kinetic energy of mass \(6\mathrm{~kg}\) is \(3\mathrm{~J}\). Therefore, the correct option is: (C) \(3.00 \mathrm{~J}\)

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Most popular questions from this chapter

A ball of mass \(5 \mathrm{~kg}\) is striding on a plane with initial velocity of \(10 \mathrm{~m} / \mathrm{s}\). If co-efficient of friction between surface and ball is \((1 / 2)\), then before stopping it will describe \(\ldots \ldots\) \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(12.5 \mathrm{~m}\) (B) \(5 \mathrm{~m}\) (C) \(7.5 \mathrm{~m}\) (D) \(10 \mathrm{~m}\)

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion: In the elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason: In the elastic collision the linear momentum of the system is conserved. (A)1 (B) 2 (C) 3 (D) 4

The potential energy of a body is given by \(\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}\) (where \(\mathrm{x}\) is displacement). The magnitude of force acting on the particle is (A) constant (B) proportional to \(\mathrm{x}\) (C) proportional to \(\mathrm{x}^{2}\) (D) Inversely proportional to \(\mathrm{x}\)

A spring with spring constant \(\mathrm{K}\) when stretched through $2 \mathrm{~cm}\( the potential energy is \)\mathrm{U}\(. If it is stretched by \)6 \mathrm{~cm}$. The potential energy will be...... (A) \(6 \mathrm{U}\) (B) \(3 \mathrm{U}\) (C) \(9 \mathrm{U}\) (D) \(18 \mathrm{U}\)

A single conservative force \(\mathrm{F}(\mathrm{x})\) acts on a $2.5 \mathrm{~kg}\( particle that moves along the \)\mathrm{x}$ -axis. The potential energy \(\mathrm{U}(\mathrm{x})\) is given by \(\mathrm{U}(\mathrm{x})=\left[10+(\mathrm{x}-4)^{2}\right]\) where \(\mathrm{x}\) is in meter. \(\mathrm{At} \mathrm{x}=6.0 \mathrm{~m}\) the particle has kinetic energy of \(20 \mathrm{~J}\). what is the mechanical energy of the system? (A) \(34 \mathrm{~J}\) (B) \(45 \mathrm{~J}\) (C) \(48 \mathrm{~J}\) (D) \(49 \mathrm{~J}\)
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