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The magnitude of the impulse developed by a mass of 0.2 kg which changes its velocity from 5i^ - 3j^ + 7k^  m/s to 2i^ + 3j^ + k^ m/s is

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Explanation

Impulse  J=Δp=m(vrvi)0.2(2i^+3j^+k^)(5i^3j^+7k^)          =(0.6i^+1.2j^1.2k^)     J=(0.6)2+(1.2)2+(1.2)2               =1.8Ns

A round disc of the moment of inertia l2 about its axis perpendicular to its plane and passing through its center is placed over another disc of the moment of inertial l1 rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is

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Explanation

3.

According to the conservation of angular momentum

 l1ω1 = l2ω2  l1ω = l1 + l2ω2  ω2 = l1ωl1 + l2

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected

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Explanation

Since no external torque acts on sphere, hence its total angular momentum remains constant.

A particle of mass 5 g is moving with a uniform speed of 32cm/s in the x-y plane along the line y = 25cm. The magnitude of its angular momentum about the origin in g-cm2/s is

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Explanation

The angular momentum of a particle about an axis is given by mvr sin(θ), where m is the mass, v is the speed, r is the perpendicular distance from the axis, and θ is the angle between v and r. For the given trajectory, r = 2√5 cm and sin(θ) = 2/√10. Substituting the values, we get L = 30√10 g-cm^2/s.

Three-point masses, each of mass m are placed at the corners of an equilateral triangle of side a. The moment of inertia of this system ab5ut an axis along one Side of the triangle is

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Explanation

3.

As the mass are point masses. The M.I. of masses lying on-axis is zero.

 M.I. of the third mass abour one side as axis= m × 32a = 3ma24

A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the system

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Explanation

The mass tries to go away from the axis and, therefore, M.I. increases.

A disc is rotating With an angular speed of m. If a child sits on it, which of the following is conserved? 

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Explanation

4.

According to the principle of conservation of angular momentum, when the child sits on the rotating disc, moment of inertia changes, so angular velocity also must change so as to keep angular momentum, as there is no torque acting on the system.

The torque of a force -6i^ acting at a point r = 4j^ about origin will bee

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Explanation

τ=r×F

A particle moves in a force field given by F = r^ F r, where r is the unit vector along with the position vector r, then which is true? 

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Explanation

3.

t=r×F=r×r^F(r)=0Therefore,t=dLdt=0;L=constant

The ratio of rotational and translatory kinetic energies of the sphere is

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Explanation

3.

Rotational kinetic energyTranslatory kinetic energy=12mv2K2R212mv2=K2R2=25

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