Exams › NEET › Physics

Let t be the time passed and x be distance covered by the two ships after which the distance between them becomes shortest. Distance(s) between the ship is given by, S = √(100 − x)² + x². For S to be minimum, dS/dt = 0 ⇒ dS/dt = 1 / 9[(100 − x)² + x²]¹/² ⇒ [−2(100 − x) + 2x] = 0 ⇒ 4x − 200 = 0 ⇒ x = 50 m. So, after both the ships have covered 50 m, distance between them becomes shortest. Time taken for it, will t = x / 10 = 50 / 10 = 5hr.

1. Position vector r̄ = cosωt î + sinωt ĵ.
2. Velocity vector v̄ = −ωsinωt î + ωcosωt ĵ.
3. Acceleration vector ā = −ω² cosωt î − ω² sinωt ĵ = −ω² r̄.
4. Nothing actually moves in the direction of the angular velocity vector ω̄. The direction of ω̄ simply represents that the circular motion is taking place in a plane perpendicular to it.

Correct answer: Acceleration vector ā = −ω² cosωt î − ω² sinωt ĵ = −ω² r̄.

Solution

Option C is correct because the acceleration vector in uniform circular motion is always directed towards the center of the circle, and its magnitude is proportional to the square of the angular velocity and the radius. This matches the given expression ā = −ω² r̄.

Related NEET Physics questions

• A block is thrown with a velocity of \( 2 m / s \) (relative to ground) on a belt, which is moving with velocity \( 4 m / s \) in opposite direction of the initial velocity of block. If the block stops slipping on the belt after \( 4 s \) of the throwing then choose the correct statement(s) This question has multiple correct options
• Due to air a falling body faces a resistive force proportional to square of velocity \( v, \) consequently its effective downward acceleration is reduced and is given by \( a=g-k v^{2} \) where \( k= \) \( 0.002 m^{-1} . \) The terminal velocity of the falling body is \( (\operatorname{in} \mathrm{m} / \mathrm{s}) \)
• In the two dimensional motions:
• A ball is thrown from rear end of the compartment of train to the front end which is moving at a constant horizontal velocity. An observer \( \boldsymbol{A} \) sitting in compartment and another observer \( B \) standing on the ground draw the trajectory. They will have
• Two forces of 3 N and 4 N act at right angles to each other on a body, as shown in the figure. The magnitude of their resultant is:
• There are three particles shown in the figure as I, II and III. The velocity and acceleration vectors associated with the motion of three particles are shown. Which of the above could represent the velocity and acceleration vectors for a projectile following a parabolic path? I. II. III.

⚔️ Practice NEET Physics free + battle 1v1 →