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Physics-

General

Easy

Question

A small object of uniform density roll up a curved surface with an initial velocity $v$ . If reaches up to a maximum height of $fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction$ with respect to the initial position. The object is

Ring
Solid sphere
Hollow sphere
Disc

The correct answer is: Disc

$fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction I open parentheses fraction numerator v over denominator R end fraction close parentheses to the power of 2 end exponent equals m g open parentheses fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction close parentheses$
$therefore I equals fraction numerator 1 over denominator 2 end fraction m R to the power of 2 end exponent$
$therefore$ Body is disc.

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A uniform rod $A B$ of length $l$ and mass $m$ is free to rotate about point $A$ . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $fraction numerator m l to the power of 2 end exponent over denominator 3 end fraction$ , the initial angular acceleration of the rod will be

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physics-General

Assertion (A): If the system of equations $3 x minus 2 y plus z equals 0 comma lambda x minus 14 y plus 15 z equals 0 comma x plus 2 y minus 3 z equals 0$ have non zero solution then $lambda equals 5$
Reason (R): If the system of equations $A X equals 0$ has a non zero solution then $bold italic A$ is singular

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For such questions, we should know area of different shapes.

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For such questions, we should know area of different shapes.

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