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This question has Statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.
Statement – I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f open parentheses 1 half mv squared close parentheses comma space then space straight f space equals space open parentheses fraction numerator straight m over denominator straight M plus straight m end fraction close parentheses
Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

  • Statement – I is true, Statement – II is true, Statement – II is a correct explanation of Statement – I.

  • Statement – I is true, Statement – II is true, Statement – II is not a correct explanation of Statement – I.

  • Statement – I is true, Statement – II is false.

  • Statement – I is true, Statement – II is false.


D.

Statement – I is true, Statement – II is false.

Before collision, the mass is m and after collision, the mass is m+M
therefore, Maximum energy loss

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From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is


C.

Consider the cross-sectional view of a diametric plane as given the figure.
Using geometry of the cube



Volume density of the solid sphere


Moment of inertia of the cube about the given axis is 

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A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is

  • fraction numerator 2 Bωl cubed over denominator 2 end fraction
  • fraction numerator 3 Bωl cubed over denominator 2 end fraction
  • fraction numerator 4 Bωl squared over denominator 2 end fraction
  • fraction numerator 4 Bωl squared over denominator 2 end fraction

D.

fraction numerator 4 Bωl squared over denominator 2 end fraction

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A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension

  • angular momentum is conserved

  • angular momentum changes in magnitude but not in the direction

  • angular momentum changes in direction but not in magnitude

  • angular momentum changes in direction but not in magnitude


C.

angular momentum changes in direction but not in magnitude

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From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is :

  • h2/4R

  • 3h/4

  • 5h/8

  • 3h2/8R


B.

3h/4

We know that centre of mass of uniform solid cone of height h is at height h/4 from base therefore,




h-zo = h/4
zo = h-h/4 = 3h/4

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