A machine gun fires 300 bullets per minute. If the mass of each bullet is \(10g\) and the velocity of the bullets is \(600 { m/s}\), the power (in kW) of the gun is:
Show Hint
- \(43200\)
- \(9\)
- \(72\)
- \(7.2\)
The Correct Option is B
Solution and Explanation
Step 1: Understanding Power Calculation The power of the gun is given by the rate of change of kinetic energy: \[ P = \frac{\Delta KE}{\Delta t} \] The kinetic energy of a single bullet is: \[ KE = \frac{1}{2} m v^2 \] where: \( m = 10g = 10 \times 10^{-3} { kg} \) (mass of one bullet), \( v = 600 { m/s} \) (velocity of bullet).
Step 2: Finding the Kinetic Energy of One Bullet \[ KE = \frac{1}{2} \times (10 \times 10^{-3}) \times (600)^2 \] \[ = \frac{1}{2} \times 0.01 \times 360000 \] \[ = \frac{3600}{2} = 1800 { J} \]
Step 3: Finding Power Output The gun fires 300 bullets per minute, i.e., 5 bullets per second: \[ P = 5 \times 1800 \] \[ = 9000 { W} = 9 { kW} \] Thus, the correct answer is: \[ P = 9 { kW} \]
Top BITSAT Physics Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
Top BITSAT thermal properties of matter Questions
- A piece of metal weighs $45 \, g$ in air and $25 \, g$ in a liquid of density $1.5 \times 10^3 \, kg-m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ}C$, the metal piece weighs $27\, g$. The density of liquid at $40^{\circ}C$ is $1.25 \times 10^3 \, kg-m^{-3}$. The coefficient of linear expansion of metal is
The stopping potential (\(V_0\)) versus frequency (\(\nu\)) of a graph for the photoelectric effect in a metal is given. From the graph, the Planck's constant (\(h\)) is:
- A submarine A, traveling at \(17 { m/s}\), is being chased along the line of its velocity by another submarine B, traveling at \(34 { m/s}\). Submarine B sends a sonar signal of \(600 { Hz}\) to detect A and receives a reflected sound of frequency \( v \). The value of \( v \) is: \[ {[Speed of sound in water} = 1500 { m/s}] \]
- Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B, and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is:
In the diagram shown below, both the strings AB and CD are made of the same material and have the same cross-section. The pulleys are light and frictionless. If the speed of the wave in string AB is \( v_1 \) and in CD is \( v_2 \), then the ratio \( \frac{v_1}{v_2} \) is:
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?