The horizontal range of a projectile fired at an angle of 15^o is 50 m. If it is fired with the same speed at an angle of 45^o, its range will be

1. 60 m

2. 71 m

3. 100 m

4. 141 m

In a two-dimensional motion, instantaneous speed ${\mathrm{v}}_0$ is a positive constant. Then which of the following is necessarily true?

1. The average velocity is not zero at any time.

2. Average acceleration must always vanish.

3. Displacements in equal time intervals are equal.

4. Equal path lengths are traversed in equal intervals.

In a two-dimensional motion, instantaneous speed ${\mathrm{v}}_0$ is a positive constant. Then which of the following is necessarily true?

1. The acceleration of the particle is zero.

2. The acceleration of the particle is increasing.

3. The acceleration of the particle is necessarily in the plane of motion.

4. The particle must be undergoing a uniform circular motion.

A particle slides down a frictionless parabolic track starting from rest at point A. Point B is at the vertex of the parabola and point C is at a height less than that of point A. After C, the particle moves freely in the air as a projectile. If the particle reaches the highest point at P, then

1. KE at P = KE at B

2. height at P = height at A

3. total energy at P = total energy at A

4. time of travel from A to B = time of travel from B to P

The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.

(a) v_av = 1/2 [v(t₁) + v(t₂)]

(b) v_av = r(t₂)-r(t₁)/t₂-t₁

(c) r = 1/2 [v(t₂)-v(t₁)](t₂-t₁)

(d) a_av = v(t₂)-v(t₁)/t₂-t₁

The incorrect alternative/s is/are:

1. (a, d)

2. (a, c)

3. (b, c)

4. (a, b)

For a particle performing uniform circular motion,

(a) Magnitude of particle velocity (speed) remains constant.

(b) Particle velocity remains directly perpendicular to the radius vector.

(c) Direction of acceleration keeps changing as the particle moves.

(d) Angular momentum is constant in magnitude but direction keeps changing.

Choose the correct statement/s:

1. (c, d)

2. (a, c)

3. (b, c)

4. (a, b, c)

Two particles are projected in the air with speed v₀, at angles θ₁ and θ₂ to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then:

(a) the angle of the project: q₁ > q₂

(b) the time of flight: T₁ > T₂

(c) the horizontal range: R₁ > R₂

(d) the total energy: U₁ > U₂

Choose the correct option:

1. (a, c, d)

2. (a, c)

3. (b, c, d)

4. (a, b, c)