Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms^-2) 

If a particle executes uniform circular motion, choose the correct statement

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

A particle has its position moved from \(\overset { \rightarrow }{ { r }_{ 1 } } =3\hat { i } +4\hat { j } \) to \(\overset { \rightarrow }{ { r }_{ 2 } } =\hat { i } +2\hat { j } \) Calculate the displacement vector (\(\Delta \)\(\overrightarrow { r } \)) and draw the \(\overrightarrow { { r }_{ 1 } } \), \(\overrightarrow { { r }_{ 2 } } \) and \(\Delta \overrightarrow { r } \) vector in a two dimensional cartesian coordinate system.

A particle is projected at an angle of θ with respect to the horizontal direction. Match the following for the above motion.
(a) v_x - decreases and increases
(b) v_y - remains constant
(c) Acceleration - varies
(d) Position vector - remains downward

Two vectors are given as \(\vec r=2\hat i+3\hat j+5\hat k\) and \(\vec F=3\hat i-2\hat j+4\hat k\). Find the resultant vector \(\vec { \tau } =\vec { r } \times \vec { F } \).

A train 100 m long is moving with a speed of 60 km h^-1. In how many seconds will it cross a bridge of 1 km long?

Define acceleration.

An athlete covers 3 rounds on a circular track of radius 50 m. Calculate the total distance and displacement travelled by him.

The velocity of three particles A, B, C are given below. Which particle travels at the greatest speed?
\(\vec {v_A}=3\hat i+5\hat j+2\hat k\)
\(\vec {V_B}=\hat i+2\hat j+3\hat k\)
\(\vec{V_C}=5\hat i+3\hat j+4\hat k\)

A particle moves in a circle of radius 10 m. Its linear speed is given by v = 3t where t is in second and v is in ms^-1.
(a) Find the centripetal and tangential acceleration at t = 2 s.
(b) Calculate the angle between the resultant acceleration and the radius vector.

In the cricket game, a batsman strikes the ball such that it moves with the speed 30 ms^-1 at an angle 30° with the horizontal as shown in the figure. The boundary line of the cricket ground is located at a distance of 75 m from the batsman? Will the ball go for a six? (Neglect the air resistance and take acceleration due to gravity g = 10 m s^-2).