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A 5kg stationary bomb is exploded in thr...

A 5kg stationary bomb is exploded in three parts having masses in the ratio `1: 1:3`. Parts having same mass move in perpendicular directions with velocity 39m/s, then the velocity of bigger part will be

A

`(10 sqrt2)/(3) m//s`

B

`(10)/(sqrt2) m//s`

C

`13 sqrt2 m//s`

D

`15 sqrt2 m//s`

Text Solution

Verified by Experts

The correct Answer is:
C
Momentum is conserved in the event of explosion `therefore p_(3)^(2)= p_(1)^(2) + p_(2)^(2)`
Let the mass of the three parts be m, m and 3m
`(3mv_(3))^(2)= (m xx 39)^(2) + (mxx 39)^(2) rArr 39 sqrt2 = 3v_(3), v_(3)= 13 sqrt2 m//s`
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Knowledge Check

  • A 5 kg stationary bomb is exploded in three parts having masses in the ratio 1 : 1: 3. Parts having same mass move in perpendicuiar directions with velocity 39 m/s, then the velocity of bigger part will be

    A
    `(10sqrt2)/3`m/s
    B
    `(10)/sqrt2`m/s
    C
    `13sqrt2`m/s
    D
    `15sqrt2m//s`

  • A stationary body of mass 3kg explodes into three equal places. Two of the places fly off in two mutually perpendicular directions, one with a velocity of 3 hat i ms^-1 and the other with a velcotiy of 4 hat j ms^-1 , If the explosion occurs in 10^-4 s , the average force acting on the third place in newton is

    A
    `(3 hat i+4 hat j) times 10^-4`
    B
    `(3 hat i-4 hat j) times 10^-4`
    C
    `(3hat i+4 hat j) times 10^4`
    D
    `-(3 hat i+4 hat j) times 10^4`

  • A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicular each after with a velocity of 12 m/s, then the velocity of the third part which has 3 times mass of each part is

    A
    `4sqrt(2) m//s` at an angle of `45^@` from each body
    B
    `24sqrt(2) m//s` at an angle of `135^@` from each body
    C
    `6sqrt(2) m//s` at `135^@` from each body
    D
    `4sqrt(2) m//s` at `135^@` from each body

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