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  • Given below are two statements:One is labelled as Assertion A and the other is labelled as Reason R Assertion A: Two identical balls A a

Given below are two statements:One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Two identical balls A and B thrown with same velocity \mathrm{'u'} at two different angles with horizontal attained the same \mathrm{h_{1}}range R. If A and B reached the maximum height \mathrm{h_{1}} and \mathrm{h_{2}} respectively,then \mathrm{R=4\sqrt{h_{1}h_{2}}}

Reason R: Product of said heights.

\mathrm{h_{1}h_{2}=\left ( \frac{u^{2}\sin^{2}\theta}{2g} \right ).\left ( \frac{u^{2}\cos^{2} \theta}{2g} \right )}

Question: Choose the correct answer:

Option: 1

Both A and R are true and R is the correct explanation of A.


Option: 2

Both A and R are true but R is the NOT the correct explanation of A.


Option: 3

A is true but R is false.


Option: 4

A is false but R is true.


Answers (1)

best_answer

For two balls \mathrm{A\: and \: B} thrown with the same velocity \mathrm{'u'} at two different angles with horizontal obtained the same range \mathrm{R} then their angles of projection let say \mathrm{\alpha \: and \: \beta } respectively will have a relation

\mathrm{\alpha+\beta=90^{\circ}}\\

If  \mathrm{ \alpha=\theta, } then \mathrm{ \beta=90- \alpha=90 - \theta }

\mathrm{h_{1}=\frac{u^{2} \sin \theta}{2 g} ; h_{2}=\frac{u^{2} \sin (90-\theta)}{2 g}}\\

                          \mathrm{h_{2}=\frac{u^{2} \cos \theta}{2 g}}\\

\mathrm{R=\frac{2 u \sin \theta \cos \theta}{g}=4 \sqrt{h_{1} h_{2}}}

Hence the correct answer is option 1.

Posted by

vishal kumar

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