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JEE PHYSICS MCQ: MOTION IN PLANE

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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 and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height

{h_1}

and

{h_2}

respectively, then

R = 4\sqrt {{h_1}{h_2}}

Reason R: Product of said heights.

{h_1}{h_2} = \left( {\frac{{{u^2}{{\sin }^2}\theta }}{{2g}}} \right).\left( {\frac{{{u^2}{{\cos }^2}\theta }}{{2g}}} \right)

Choose the correct answer:

View answer and explanation

Correct option: A

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

Option A is correct. The range is related to the maximum heights by the formula

R = 4\sqrt{h_1 h_2}

, and the product of the heights leads to this relationship.

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\mathrm{\vec P} = \mathrm{\vec A} + \mathrm{\vec B}\,\,\mathrm{and}\,P = A + B.

The angle between

\mathrm{\vec A}\,and\,\mathrm{\vec B}

is Assertion: The necessary condition for motion in two dimensions, velocity and acceleration vectors should have any angle between

0^{\circ}

90^{\circ}

between them.
Reason: For two-dimensional or three-dimensional motion, velocity and acceleration of an object works in opposite direction.

\mathrm{If}\,(\mathbf{a}+3 \mathbf{b}) \cdot(7 \mathbf{a}-5 \mathbf{b})=0

(\mathbf{a}-4 \mathbf{b}) \cdot(7 \mathbf{a}-2 \mathbf{b})=0

. Then, the angle between

\mathbf{a}

\mathbf{b}

is At the top of the trajectory of a projectile, the direction of its velocity and acceleration are A ball is thrown at an angle

\theta

and another ball is thrown at an angle

\left(90^{\circ}-\theta\right)

with the horizontal direction from the same point with velocity

39.2 \mathrm{~ms}^{-1}

. The second ball reaches

50 \mathrm{~m}

higher than the first ball. Find their individual heights. Take

{g}=9.8 \mathrm{~ms}^{-2}

. Assertion: The drover in a vehicle moving with a constant speed on a straight road is in a non-inertial frame of reference.

Reason: A reference frame in which Newton's laws of motion are applicable is non-inertial.