Home
Class 11
PHYSICS
A bombshell of mass explodes such that t...

A bombshell of mass explodes such that the broken masses are in the ratio `1 : 1 : 3`. The ratio two pieces of equal mass fly with the same speed at right angles to each other with a velocity of `100ms^(-1)`. Find the direction and velocity of the third fragment of the shell. What will be the total kinetic energy of the fragments.

Text Solution

Verified by Experts

Assume mass of the shell `=m`
Given, `m_(1) : m_(2) : m_(3) : 1 : 1 : 3 `
i.e. `m_(1)=m_(2)=(1)/(5)m` and `m_(3)=(3)/(5)m`
We know that
`0=m_(2)vcos0+m_(1)vcos90^(@)+m_(3)v_(3)cos225^(@)`
i.e. `0=(m)/(5)v+0+(3)/(5)mv_(3)(-(1)/(sqrt(2)))`
i.e. `v=(3)/(sqrt(2))v_(3)`
Given , `v=100ms^(-1)`, hence `v_(3)=(1.414)/(3)xx100`
`v_(3)=47.1ms^(-1)` at `225^(@)` w.r.t to the `X`axis
`KE=KE_(1)+KE_(2)+KE_(3)`
`=(1)/(2)xx(100)/(5)xx(100)^(2)+(1)/(2)xx(100)/(5)xx(100)^(2)+(1)/(2)xx(3)/(5)xx100xx(47.1)^(2)`
`=(1)/(10)(10^(6)(1+1+0.22)`
`:.KE=2.22xx10^(5)J`.
Promotional Banner

Topper's Solved these Questions

  • LAWS OF MOTION

    SUBHASH PUBLICATION|Exercise Five mark question|4 Videos

  • KINETIC THEORY

    SUBHASH PUBLICATION|Exercise NUMERICALS WITH SOLUTIONS|19 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    SUBHASH PUBLICATION|Exercise NUMERICALS WITH SOLUTIONS|33 Videos

Similar Questions

Explore conceptually related problems

A body of mass m at rest gets exploded into 3 parts, having masses in the ratio 1: 1:3. Its two parts having equal masses move at right angles to each other with 15 m/s each. The velocity of third is:

Calculate the de Broglie wavelength of a bullet of mass 25g moving with a velocity of 100ms^(-1) .

A body of mass 5 kg explodes into 3 fragments having masses in the ratio of 2:2 : 1. The fragments with equal masses fly in merely far direction with speed 15 ms^(-1) . What will be the velocity of lighter one ?

A shell of mass 15 kg, initially a rest, explodes into three fragments of masses in the ratio 1:1: 3. The fragments with equal masses fly off in mutually perpendicular directions with a speed of 6 ms^(-1) The speed of the heaviest fragment will be :

A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3 .The smaller fragment moves with a velocity of 6 ms^(-1) .The kinetic energy of the larger fragment is

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off at right angles to each other, one with a velocity of 2 i m/s and the other with a velocity of 3 j m/s. If the explosion takes place in 10^(5)s , the average force acting on the third piece in newton is:

A cricket ball of mass 0-5 kg strikes a bat normally with a velocity of 30 ms^(-1) and rebounds with a velocity of 20 ms^(-1) in the opposite direction. The impulse of the force exerted by the ball on the bat is :

Find the mass of an electrically charged particle movng with a velocity of 3xx 10^(6) ms^(-1) and having a de Brogue wavelength of 2Å.