Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEETPhysicsMotion in Two Dimensions

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 h 1 h 2 Reason R: Product of said heights. h 1 h 2 = u 2 sin 2 θ 2 g · u 2 cos 2 θ 2 g

Options

  1. ABoth A and R are true and R is the correct explanation of A.
  2. BBoth A and R are true but R is NOT the correct explanation of A.
  3. CA is true but R is false.
  4. DA is false but R is true.

Correct answer

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

Step-by-step solution

Range of two balls are R 1 = u 2 sin 2 θ 1 g = R 2 = u 2 sin 2 θ 2 g . Now, maximum height by both balls are h 1 = u 2 sin 2 θ 1 2 g and h 2 = u 2 cos 2 θ 2 2 g ∴ h 1 h 2 = u 2 sin 2 θ 2 g u 2 cos 2 θ 2 g = u 2 sin θ cos θ 2 g = R 4 ⇒ R = 4 h 1 h 2 Hence, both A and R are true and R is the correct explanation of A.

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle moving with uniform speed in a circular path maintains: 2024A bob is whirled in a horizontal plane by means of a string with an initial speed of rpm. The tension in the string is T . If speed becomes 2 while keeping the same radius, the ten 2024A particle is executing uniform circular motion with velocity v and acceleration a . Which of the following is true? 2023A ball is projected from point A with velocity 20 ~m ~s ⁻¹ at an angle 60^ to the horizontal direction. At the highest point B of the path (as shown in figure), the velocity v ~m ~ 2023A bullet is fired from a gun at the speed of   280   m   s - 1 in the direction 30 ° above the horizontal. The maximum height attained by the bullet is ( g = 9 2023A constant torque of 100 ~N ~m turns a wheel of moment of inertia 300 ~kg ~m ^2 about an axis passing through its centre. Starting from rest, its angular velocity after 3 ~s is 2023A ball is projected with a velocity, 10   m   s - 1 , at an angle of 60 ° with the vertical direction. Its speed at the highest point of its trajectory will be 2022A cricket ball is thrown by a player at a speed of 20 ~m / s in a direction 30^ above the horizontal. The maximum height attained by the ball during its motion is (g=10 ~m / s ^2 ) 2022 Full Motion in Two Dimensions list All NEET PYQs