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STATEMENT - 1 : If the velocity of centr...

STATEMENT - 1 : If the velocity of centre of mass of a system is zero then the kinetic energy of the system may be greater than zero.
and
STATEMENT - 2 : Kinetic energy of the system is given by `(1)/(2)int v^(2)dm`, where dm is mass of element and v is its speed.

A

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1.

B

Statement - 1 is True, Statement - 2 is True, Statement - 2 is NOT a correct explanation for statement - 1.

C

Statement - 1 is True, Statement - 2 is False.

D

Statement - 1 is False, Statement - 2 is True.

Text Solution

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The correct Answer is:
A
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STATEMENT-1 : The total momentum of a system in C -frame is always zero. and STATEMENT-2 : The total kinetic energy of a system in C -frame is always zero.

Two particles having masses m_(1) and m_(2) are moving with velocities vec(V)_(1) and vec(V)_(2) respectively. vec(V)_(0) is velocity of centre of mass of the system. (a) Prove that the kinetic energy of the system in a reference frame attached to the centre of mass of the system is KE_(cm) = (1)/(2)mu V_(rel)^(2) . Where mu=(m_(1)m_(2))/(m_(1)+m_(2)) and V_(rel) is the relative speed of the two particles. (b) Prove that the kinetic energy of the system in ground frame is given by KE=KE_(cm)+(1)/(2)(m_(1)+m_(2))V_(0)^(2) (c) If the two particles collide head on find the minimum kinetic energy that the system has during collision.

Knowledge Check

  • A : If net force acting-on a system is zero, then work done on the system may be nonzero. R : Internal forces acting on a system can increase its kinetic energy.

    A
    If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
    B
    If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
    C
    If Assertion is true statement but Reason is false, then mark (3).
    D
    If both Assertion and Reason are falsė statements, then mark (4).

  • Assertion : Net external force acting on a system of particles is zero but it possible that kinetic energy of the system increases . Reason : Kinetic energy of the system can be changed by internal forces of the system .

    A
    If both assertion and reason are corret and reason is a correct explanation of the assertion .
    B
    If both assertion and reason are correct but reason is ot the correct explanation of assertion .
    C
    If assertion is correct but reason is incorrect .
    D
    If both assertion and reason are incorrect .

  • Consider the following two statements. I. The linear momentum of a system of particles is zero. II. The kinetic energy of a system of particles is zero. Then

    A
    I implies II and II implies I.
    B
    I does not imply II and II does not imply I.
    C
    I implies II but II does not imply I
    D
    I does not imply II but II implies I.

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