If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. a_r = 0 and a_t = 0
2. a_r = 0 but a_t \(\neq\) 0
3. a_r \(\neq\) 0 but a_t = 0
4. a_r \(\neq\) 0 and a_t \(\neq\) 0$\mathrm{}$
 

The figure shows a body of mass m moving with a uniform speed v along a circle of radius r. The change in velocity in going from A to B is:

1. $v\sqrt{2}$

2. $v/\sqrt{2}$

3. v

4. zero

An aeroplane is flying horizontally with a velocity u = 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:

1. 1200 m

2. 0.33 km

3. 3.33 km

4. 33 km

A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a speed of 5 m/sec from the same height. The correct statement is:

(1) Both particles will reach at ground simultaneously

(2) Both particles will reach at ground with same speed

(3) Particle (A) will reach at ground first with respect to particle (B)

(4) Particle (B) will reach at ground first with respect to particle (A)

An object is thrown along a direction inclined at an angle of 45° with the horizontal direction. The horizontal range of the particle is equal to 

(1) Vertical height

(2) Twice the vertical height

(3) Thrice the vertical height

(4) Four times the vertical height

If the range of a gun that fires a shell with muzzle speed v is R, then the angle of elevation of the gun is 

(1) ${\cos }^{-1}\left(\frac{{\displaystyle v^2}}{{\displaystyle Rg}}\right)$

(2) ${\cos }^{-1}\left(\frac{{\displaystyle gR}}{{\displaystyle v^2}}\right)$

(3) $\frac{1}{2}\left(\frac{{\displaystyle v^2}}{{\displaystyle Rg}}\right)$

(4) $\frac{1}{2}{\sin }^{-1}\left(\frac{{\displaystyle gR}}{{\displaystyle v^2}}\right)$

Four bodies \(P\), \(Q\), \(R\) and \(S\) are projected with equal velocities having angles of projection \(15^{\circ},\) \(30^{\circ},\)\(45^{\circ},\) and \(60^{\circ}\) with the horizontal respectively. The body having the shortest range is? 

Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event?
1. speed before he jumps and his weight
2. the direction in which he leaps and the initial speed
3. the force with which he pushes the ground and his speed
4. none of the above

The equation of motion of a projectile is given by x = 36 t metre and 2y = 96 t – 9.8 t² metre. The angle of projection is:

1. ${\sin }^{-1}\left(\frac{{\displaystyle 4}}{{\displaystyle 5}}\right)$

2. ${\sin }^{-1}\left(\frac{{\displaystyle 3}}{{\displaystyle 5}}\right)$

3. ${\sin }^{-1}\left(\frac{{\displaystyle 4}}{{\displaystyle 3}}\right)$

4. ${\sin }^{-1}\left(\frac{{\displaystyle 3}}{{\displaystyle 4}}\right)$

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

(1) $t_1{t}_2\propto R^2$

(2) $t_1{t}_2\propto R$

(3) $t_1{t}_2\propto \frac{1}{R}$

(4) $t_1{t}_2\propto \frac{1}{R^2}$