A particle slides down on a smooth incline of inclination 30°, fixed in an elevator going up with an acceleration 2 m/s². The box of incline has a length 4m. The time taken by the particle to reach the bottom will be

• ( 8/9 ) √3 s

• ( 9/8 ) √3 s

• ( 4/3 ) √(√3/2 ) s

• ( 3/4 ) √(√3/2 ) s

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle $\left(\frac{\mathrm{\pi }}{2} - \mathrm{\theta }\right)$ with the horizontal, it reaches maximum height H₂. The relation between the horizontal range R of the projectile, H₁ and H₂ is 

• R = $4 \sqrt{{\mathrm{H}}_1 {\mathrm{H}}_2}$

• R = 4 ( H₁ - H₂ )

• R = 4( H₁ + H₂ )

• R = $\frac{{\mathrm{H}}_1^2}{{\mathrm{H}}_2^2}$

A projectile is given an initial velocity of î + 2 ĵ . The cartesian equation of its path is ( Take g = 10 ms² )

• y = x - 5x²

• y = 2x - 5x²

• y = 2x - 15x²

• y = 2x - 25x²

164.

If  $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are non-zero vectors which obey the relation  $\left| \overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}} \right| = \left| \overrightarrow{\mathrm{A}} - \overrightarrow{\mathrm{B}} \right|$, then the angle between them is

• 0^o

• 60^o

• 90^o

• 120^o

An arrow is projected into air. Its time of flight is 5 s and range 200 m. What is the maximum height reached by it? ( Take g= 10 ms^-2 )

• 31·25 m

• 24·5 m

• 18·25 m

• 46·75 m

A particle moves in a circular path with decreasing speed. Choose the correct statement.

• Angular momentum remains constant

• Acceleration $\overrightarrow{\mathrm{\alpha }}$ is towards the centre

• Particle moves in a spiral path with decreasing radius

• The direction of angular momentum remains constant

A particle is projected from the ground with an initial speed of 'v' at angle θ  with horizontal. The average velocity of the particle between its point of projection and height point of trajectory is

• 

• 

• 

• vcosθ

Two projectiles of same mass have their maximum kinetic energies in ratio 4:1 and ratio of their maximum height is also 4:1 then what is the ratio of their ranges?

• 2 : 1

• 4 : 1

• 8 : 1

• 16 : 1

In figure, a particle having mass m = 5 g and large  q'= 2 x 10^-9  starts from rest at point  $𝑎$ and moves in a straight line to point b. What is its speed  v at point  b?

• 2.65 cms^-1

• 3.65 cms^-1

• 4.65 cms^-1

• 5.65 cms^-1

Assertion: Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed. 

Reason: The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion is true but reason is false.