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There is an object of mass 5m kept at...

There is an object of mass 5m kept at rest in space. Suddenly it explodes in three parts of masses m , 2m and 2m . Two parts of equal masses are found to move with equal speeds v along perpendicular directions . If energy released in explosion is `nmv^(2)` , then find value of n .

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To solve the problem step-by-step, we will use the principles of conservation of momentum and kinetic energy. ### Step 1: Understand the system We have an object of mass \(5m\) at rest. It explodes into three parts with masses \(m\), \(2m\), and \(2m\). The two parts of mass \(2m\) move with equal speeds \(v\) along perpendicular directions. ### Step 2: Apply conservation of momentum Since the initial momentum of the system is zero (the object is at rest), the total momentum after the explosion must also be zero. ...
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Knowledge Check

  • A particle of mass 4 m which is at rest explodes into masses m, m & 2m . Two of the fragments of masses m and 2m are found to move with equal speeds v each in opposite directions. The total mechanical energy released in the process of explosion is :-

    A
    `mv^(2)`
    B
    `2mv^(2)`
    C
    `1//2mv^(2)`
    D
    `4mv^(2)`

  • An object is kept at rest . Object explodes in two parts of unequal masses .

    A
    Both parts move in the same direction
    B
    Both parts move in same direction but along different lines .
    C
    Both parts move in opposite directions with same speed .
    D
    Both parts move in opposite directions with different speed .

  • An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are 2phati and phatj . The momentum of the third part

    A
    will have a magnitude `psqrt3`
    B
    will have a magnitude `psqrt5`
    C
    will have a magnitude p
    D
    will have a magnitude 2p.

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