AIEEE 2010 | Rotational Motion Question 189 | Physics

A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}$$ in the $$x$$-$$y$$ plane as shown in the figure. At a time $$t < {{{v_0}\sin \theta } \over g},$$ the angular momentum of the particle is ................,

AIEEE 2010 Physics - Rotational Motion Question 178 English

AIEEE 2010 Physics - Rotational Motion Question 178 English

where $$\widehat i,\widehat j$$ and $$\widehat k$$ are unit vectors along $$x,y$$ and $$z$$-axis respectively.

$$ - mg\,{v_0}{t^2}\cos \theta \widehat j$$

$$mg\,{v_0}t\cos \theta \widehat k$$

$$ - {1 \over 2}mg\,{v_0}{t^2}\cos \,\theta \widehat k$$

$${1 \over 2}mg\,{v_0}{t^2}\cos \theta \widehat i$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

A thin uniform rod of length $$l$$ and mass $$m$$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\omega $$. Its center of mass rises to a maximum height of:

$${1 \over 6}\,\,{{l\omega } \over g}$$

$${1 \over 2}\,\,{{{l^2}{\omega ^2}} \over g}$$

$${1 \over 6}\,\,{{{l^2}{\omega ^2}} \over g}$$

$${1 \over 3}\,\,{{{l^2}{\omega ^2}} \over g}$$

AIEEE 2008

MCQ (Single Correct Answer)

-1

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

$${5 \over 6}m{a^2}$$

$${1 \over 12}m{a^2}$$

$${7 \over 12}m{a^2}$$

$${2 \over 3}m{a^2}$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rolls down (without slipping) an inclined plane making an angle $$\theta $$ with the horizontal. Then its acceleration is

$${{g\,\sin \theta } \over {1 - M{R^2}/I}}$$

$${{g\,\sin \theta } \over {1 + I/M{R^2}}}$$

$${{g\,\sin \theta } \over {1 + M{R^2}/I}}$$

$${{g\,\sin \theta } \over {1 - I/M{R^2}}}$$

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