(D) Let $u$ be the velocity of the bullet with respect to the car.The rate of mass ejection $\frac{dm}{dt}$ is the mass thrown per second by the machi

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Let $u$ be the velocity of the bullet with respect to the car.The rate of mass ejection $\frac{dm}{dt}$ is the mass thrown per second by the machine gun.$\frac{dm}{dt} = \text{Mass of one bullet} \times \text{Number of bullets fired per second}$$\frac{dm}{dt} = 10 \,g \times 10 \,bullets/s = 100 \,g/s = 0.1 \,kg/s$.The thrust force $F$ exerted on the car is given by $F = u \frac{dm}{dt}$.$F = 500 \,m/s \times 0.1 \,kg/s = 50 \,N$.The acceleration $a$ of the car is given by $a = \frac{F}{M}$,where $M$ is the mass of the car.$a = \frac{50 \,N}{2000 \,kg} = \frac{1}{40} \,m/s^2 = 0.025 \,m/s^2$.

Class 11 Physics Newton's Laws of Motion and Friction Variable Mass System and Rocket Problem

Medium

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. If the number of bullets fired per second is $10$,the acceleration of the car will be ..... $m/s^2$.

A
$0.25$
B
$2.5$
C
$5.0$
D
$0.025$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

Subtopic

Variable Mass System and Rocket Problem

$A$ railway wagon of mass $5 \times 10^3 \ kg$ is moving with an initial velocity of $1.2 \ m/s$ on frictionless rails. Rain falls vertically into the wagon. When $10^3 \ kg$ of water has collected in the wagon,what is the change in the kinetic energy of the wagon in $J$?

Difficult

View Solution

Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

Medium

View Solution

$A$ rocket has an initial mass of $20 \times 10^3 \, kg$. If it is to blast off with an initial acceleration of $4 \, m/s^2$,the initial thrust needed is $(g = 10 \, m/s^2)$.

Easy

View Solution

$A$ balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be: (Take $g$ as acceleration due to gravity)

DifficultJEE MAIN 2025

View Solution

$A$ gun of mass $10 \, kg$ fires $4$ bullets per second. The mass of each bullet is $20 \, g$ and the velocity of the bullet when it leaves the gun is $300 \, m/s$. The force required to hold the gun while firing is (in $N$)

EasyAIIMS 2016

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. If the number of bullets fired per second is $10$,the acceleration of the car will be ..... $m/s^2$.

Similar Questions

$A$ railway wagon of mass $5 \times 10^3 \ kg$ is moving with an initial velocity of $1.2 \ m/s$ on frictionless rails. Rain falls vertically into the wagon. When $10^3 \ kg$ of water has collected in the wagon,what is the change in the kinetic energy of the wagon in $J$?

Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

$A$ rocket has an initial mass of $20 \times 10^3 \, kg$. If it is to blast off with an initial acceleration of $4 \, m/s^2$,the initial thrust needed is $(g = 10 \, m/s^2)$.

$A$ balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be: (Take $g$ as acceleration due to gravity)

$A$ gun of mass $10 \, kg$ fires $4$ bullets per second. The mass of each bullet is $20 \, g$ and the velocity of the bullet when it leaves the gun is $300 \, m/s$. The force required to hold the gun while firing is (in $N$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module