A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is: (Given initial temperature of the bullet = 127°C), Melting point of the bullet = 327°C, Latent heat of fusion of lead = \(2.5 × 10^4 J kg^{–1}\) Specific heat capacity of lead = 125 J/kg K)
- \(125\;ms^{–1}\)
- \(500\;ms^{–1}\)
- \(250\;ms^{–1}\)
- \(600\;ms^{–1}\)
The Correct Option is B
Solution and Explanation
The initial speed of bullet is:
\(\frac{2}{5}×\frac{1}{2}mv^2=mL+msΔT\)
\(⇒\frac{v^2}{5}=2.5×10 ^4+125+200\)
\(⇒\frac{v^2}{5}=5×10^4\)
\(⇒ v = 500 \;m/s\)
Top Questions on Kinetic Energy
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
- JEE Main - 2025
- Physics
- Kinetic Energy
- If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is
- AP EAPCET - 2025
- Physics
- Kinetic Energy
- A body moves in a circular path with constant speed. Its kinetic energy:
- CUET (UG) - 2025
- Physics
- Kinetic Energy
- A particle of mass 2 kg moves at 3 m/s. Its kinetic energy is:
- CUET (UG) - 2025
- Physics
- Kinetic Energy
- A body of mass 4 kg is moving with a velocity of 3 m/s. What is its kinetic energy?
- AP EAPCET - 2025
- Physics
- Kinetic Energy
Questions Asked in JEE Main exam
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- permutations and combinations
- A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
- JEE Main - 2025
- Magnetic Field
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Complex numbers
Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
