Explosion of Bodies
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365828 A body of mass \(M\) splits into two parts \(\alpha M\) and \((1-\alpha) M\) by an internal explosion, which generates kinetic energy \(T\). After explosion if the two parts move in the same direction as before, their relative speed will be

1 \(\sqrt{\dfrac{2 T}{\alpha(1-\alpha) M}}\)
2 \(\sqrt{\dfrac{T}{(1-\alpha) M}}\)
3 \(\sqrt{\dfrac{2 T}{(1-\alpha) M}}\)
4 \(\sqrt{\dfrac{T}{2(1-\alpha) M}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365829 A block moving in air explodes into two parts then just after explosion (neglect change in momentum due to gravity)

1 The total momentum of two parts must be same to the momentum of the block before explosion.
2 The total momentum must change.
3 The total kinetic energy of two parts must be same to the momentum of the block before explosion.
4 The total kinetic energy must be constant.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365830 \({ }_{84}^{210} X\) originally at rest emits \(\alpha\)-particles of kinetic energy K. Find the \(K E\) of recoiling nucleus.

1 \(\dfrac{4}{206} K\)
2 \(\dfrac{4}{214} K\)
3 \(\dfrac{K}{214} K\)
4 \(\dfrac{K}{206}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365831 A stationary body of mass \(m\) gets exploded in 3 parts having mass in the ratio of \(1: 3: 3\). Its two fractions having equal mass moving at right angle to each other with velocity of \(15\;m/\sec \). Then the velocity of the third body is :-

1 \(45 \sqrt{(2)} m / \mathrm{sec}\)
2 \(5\sqrt {(32)} m/\sec \)
3 \(5 \mathrm{~m} / \mathrm{sec}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365832 A bomb of mass \(9\;kg\) explodes into 2 pieces of mass \(3\;kg\) and \(6\;kg\). The velocity of mass \(3\;kg\) is \(1.6\;\,m/s,\) the \(K.E\) of mass \(6\;kg\) is

1 \(9.6 \mathrm{~J}\)
2 \(3.84 \mathrm{~J}\)
3 \(2.92 \mathrm{~J}\)
4 \(1.92 \mathrm{~J}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365828 A body of mass \(M\) splits into two parts \(\alpha M\) and \((1-\alpha) M\) by an internal explosion, which generates kinetic energy \(T\). After explosion if the two parts move in the same direction as before, their relative speed will be

1 \(\sqrt{\dfrac{2 T}{\alpha(1-\alpha) M}}\)
2 \(\sqrt{\dfrac{T}{(1-\alpha) M}}\)
3 \(\sqrt{\dfrac{2 T}{(1-\alpha) M}}\)
4 \(\sqrt{\dfrac{T}{2(1-\alpha) M}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365829 A block moving in air explodes into two parts then just after explosion (neglect change in momentum due to gravity)

1 The total momentum of two parts must be same to the momentum of the block before explosion.
2 The total momentum must change.
3 The total kinetic energy of two parts must be same to the momentum of the block before explosion.
4 The total kinetic energy must be constant.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365830 \({ }_{84}^{210} X\) originally at rest emits \(\alpha\)-particles of kinetic energy K. Find the \(K E\) of recoiling nucleus.

1 \(\dfrac{4}{206} K\)
2 \(\dfrac{4}{214} K\)
3 \(\dfrac{K}{214} K\)
4 \(\dfrac{K}{206}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365831 A stationary body of mass \(m\) gets exploded in 3 parts having mass in the ratio of \(1: 3: 3\). Its two fractions having equal mass moving at right angle to each other with velocity of \(15\;m/\sec \). Then the velocity of the third body is :-

1 \(45 \sqrt{(2)} m / \mathrm{sec}\)
2 \(5\sqrt {(32)} m/\sec \)
3 \(5 \mathrm{~m} / \mathrm{sec}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365832 A bomb of mass \(9\;kg\) explodes into 2 pieces of mass \(3\;kg\) and \(6\;kg\). The velocity of mass \(3\;kg\) is \(1.6\;\,m/s,\) the \(K.E\) of mass \(6\;kg\) is

1 \(9.6 \mathrm{~J}\)
2 \(3.84 \mathrm{~J}\)
3 \(2.92 \mathrm{~J}\)
4 \(1.92 \mathrm{~J}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365828 A body of mass \(M\) splits into two parts \(\alpha M\) and \((1-\alpha) M\) by an internal explosion, which generates kinetic energy \(T\). After explosion if the two parts move in the same direction as before, their relative speed will be

1 \(\sqrt{\dfrac{2 T}{\alpha(1-\alpha) M}}\)
2 \(\sqrt{\dfrac{T}{(1-\alpha) M}}\)
3 \(\sqrt{\dfrac{2 T}{(1-\alpha) M}}\)
4 \(\sqrt{\dfrac{T}{2(1-\alpha) M}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365829 A block moving in air explodes into two parts then just after explosion (neglect change in momentum due to gravity)

1 The total momentum of two parts must be same to the momentum of the block before explosion.
2 The total momentum must change.
3 The total kinetic energy of two parts must be same to the momentum of the block before explosion.
4 The total kinetic energy must be constant.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365830 \({ }_{84}^{210} X\) originally at rest emits \(\alpha\)-particles of kinetic energy K. Find the \(K E\) of recoiling nucleus.

1 \(\dfrac{4}{206} K\)
2 \(\dfrac{4}{214} K\)
3 \(\dfrac{K}{214} K\)
4 \(\dfrac{K}{206}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365831 A stationary body of mass \(m\) gets exploded in 3 parts having mass in the ratio of \(1: 3: 3\). Its two fractions having equal mass moving at right angle to each other with velocity of \(15\;m/\sec \). Then the velocity of the third body is :-

1 \(45 \sqrt{(2)} m / \mathrm{sec}\)
2 \(5\sqrt {(32)} m/\sec \)
3 \(5 \mathrm{~m} / \mathrm{sec}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365832 A bomb of mass \(9\;kg\) explodes into 2 pieces of mass \(3\;kg\) and \(6\;kg\). The velocity of mass \(3\;kg\) is \(1.6\;\,m/s,\) the \(K.E\) of mass \(6\;kg\) is

1 \(9.6 \mathrm{~J}\)
2 \(3.84 \mathrm{~J}\)
3 \(2.92 \mathrm{~J}\)
4 \(1.92 \mathrm{~J}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365828 A body of mass \(M\) splits into two parts \(\alpha M\) and \((1-\alpha) M\) by an internal explosion, which generates kinetic energy \(T\). After explosion if the two parts move in the same direction as before, their relative speed will be

1 \(\sqrt{\dfrac{2 T}{\alpha(1-\alpha) M}}\)
2 \(\sqrt{\dfrac{T}{(1-\alpha) M}}\)
3 \(\sqrt{\dfrac{2 T}{(1-\alpha) M}}\)
4 \(\sqrt{\dfrac{T}{2(1-\alpha) M}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365829 A block moving in air explodes into two parts then just after explosion (neglect change in momentum due to gravity)

1 The total momentum of two parts must be same to the momentum of the block before explosion.
2 The total momentum must change.
3 The total kinetic energy of two parts must be same to the momentum of the block before explosion.
4 The total kinetic energy must be constant.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365830 \({ }_{84}^{210} X\) originally at rest emits \(\alpha\)-particles of kinetic energy K. Find the \(K E\) of recoiling nucleus.

1 \(\dfrac{4}{206} K\)
2 \(\dfrac{4}{214} K\)
3 \(\dfrac{K}{214} K\)
4 \(\dfrac{K}{206}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365831 A stationary body of mass \(m\) gets exploded in 3 parts having mass in the ratio of \(1: 3: 3\). Its two fractions having equal mass moving at right angle to each other with velocity of \(15\;m/\sec \). Then the velocity of the third body is :-

1 \(45 \sqrt{(2)} m / \mathrm{sec}\)
2 \(5\sqrt {(32)} m/\sec \)
3 \(5 \mathrm{~m} / \mathrm{sec}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365832 A bomb of mass \(9\;kg\) explodes into 2 pieces of mass \(3\;kg\) and \(6\;kg\). The velocity of mass \(3\;kg\) is \(1.6\;\,m/s,\) the \(K.E\) of mass \(6\;kg\) is

1 \(9.6 \mathrm{~J}\)
2 \(3.84 \mathrm{~J}\)
3 \(2.92 \mathrm{~J}\)
4 \(1.92 \mathrm{~J}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365828 A body of mass \(M\) splits into two parts \(\alpha M\) and \((1-\alpha) M\) by an internal explosion, which generates kinetic energy \(T\). After explosion if the two parts move in the same direction as before, their relative speed will be

1 \(\sqrt{\dfrac{2 T}{\alpha(1-\alpha) M}}\)
2 \(\sqrt{\dfrac{T}{(1-\alpha) M}}\)
3 \(\sqrt{\dfrac{2 T}{(1-\alpha) M}}\)
4 \(\sqrt{\dfrac{T}{2(1-\alpha) M}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365829 A block moving in air explodes into two parts then just after explosion (neglect change in momentum due to gravity)

1 The total momentum of two parts must be same to the momentum of the block before explosion.
2 The total momentum must change.
3 The total kinetic energy of two parts must be same to the momentum of the block before explosion.
4 The total kinetic energy must be constant.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365830 \({ }_{84}^{210} X\) originally at rest emits \(\alpha\)-particles of kinetic energy K. Find the \(K E\) of recoiling nucleus.

1 \(\dfrac{4}{206} K\)
2 \(\dfrac{4}{214} K\)
3 \(\dfrac{K}{214} K\)
4 \(\dfrac{K}{206}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365831 A stationary body of mass \(m\) gets exploded in 3 parts having mass in the ratio of \(1: 3: 3\). Its two fractions having equal mass moving at right angle to each other with velocity of \(15\;m/\sec \). Then the velocity of the third body is :-

1 \(45 \sqrt{(2)} m / \mathrm{sec}\)
2 \(5\sqrt {(32)} m/\sec \)
3 \(5 \mathrm{~m} / \mathrm{sec}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365832 A bomb of mass \(9\;kg\) explodes into 2 pieces of mass \(3\;kg\) and \(6\;kg\). The velocity of mass \(3\;kg\) is \(1.6\;\,m/s,\) the \(K.E\) of mass \(6\;kg\) is

1 \(9.6 \mathrm{~J}\)
2 \(3.84 \mathrm{~J}\)
3 \(2.92 \mathrm{~J}\)
4 \(1.92 \mathrm{~J}\)