An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio

• 1 : 2

• 2 : 1

• 1 : 4

• 4 : 1

A ball which is at rest is dropped from a height h metre. As it bounces off the floor its speed is 80% of what it was just before touching the ground. The ball will then rise to nearly a height

• 0.94 h

• 0.80 h

• 0.75 h

• 0.64 h

Two bodies of different masses are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is

• $\frac{25}{16}$

• $\frac{5}{4}$

• $\frac{4}{5}$

• $\frac{16}{25}$

The centripetal acceleration of particle of mass m moving with a velocity v in a circular orbit of radius r is

• v²/r  along the radius, towards the centre 

• v²/r along the radius, away from the centre 

• mv²/r  along the radius, away from the centre 

• mv²/r  along the radius, towards the centre 

A stationary body of mass m explodes into three parts having masses in the ratio 1 : 3 : 3. The two fractions with equal masses move at right angles to each other with a velocity of 1.5 ms^-1. Then the velocity of the third body is

• $4.5\sqrt{2} {\mathrm{ms}}^{-1}$

• 5 ms^-1

• $5\sqrt{32} {\mathrm{ms}}^{-1}$

• 1.5 ms^-1

A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to 1/3rd the escape velocity for that planet. The maximum height attained by the body is

• R/2

• R/3

• R/9

• R/8

The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

• 14

• 16

• 18

• 13

78.

Three vectors satisfy the relation A . B = 0 and A . C = 0, then A is parallel to

• C

• B

• B × C

• B . C

For a given velocity, a projectile has the same range R for two angles of projection if t₁ and t₂ are the time of flight in the two cases, then

• t₁t₂ ∝ R

• t₁t₂ ∝ R²

• ${\mathrm{t}}_1{\mathrm{t}}_2 \propto \frac{1}{{\mathrm{R}}^2}$

• ${\mathrm{t}}_1{\mathrm{t}}_2 \propto \frac{1}{\mathrm{R}}$

Look at the graphs (a) to (d) carefully and indicate which of these possibly represents one dimensional motion of a particle ?