__Objective Questions (Level 1)__

Single Correct Option

**Ques 1: A particle has initial velocity, and a constant force **

**acts on it. The path of the particle is **

**(a) straight line **

**(b) parabolic **

**(c) circular **

**(d) elliptical**

**Ans: **circular

**Sol: **

âˆ´

Path of the particle is circular.

Option (c) is correct.

**Ques 2: Identify the correct statement related to the projectile motion. **

**(a) It is uniformly accelerated everywhere **

**(b) It is uniformly accelerated everywhere except at the highest position where it is moving with constant velocity **

**(c) Acceleration is never perpendicular to velocity **

**(d) None of the above**

**Ans: **It is uniformly accelerated everywhere

**Sol: **Projectile motion is uniformly accelerated everywhere even at the highest point.

Option (a) correct.

Option (b) incorrect.

At the highest point acceleration is perpendicular to velocity.

Option (c) incorrect.

**Ques 3: A ball is projected with a velocity 20 ms -1 at an angle to the horizontal. In order to have the maximum range. Its velocity at the highest position must be **

**(a) 10 ms**^{-1}

**(b) 14 ms**^{-}^{1}

**(c) 18 ms**^{-1}

**(d) 16 ms**^{-1}

**Ans: **14 ms^{-}^{1}

**Sol: **For range to be maximum

Î¸ = 45Â°

i.e.,

or (âˆ´ v_{x} = u_{x})

= 14.14 m/s = 14 m/s (approx)

Option (b) is correct.

**Ques 4: Two bodies are thrown with the same initial velocity at angles Î¸ and (90Â° - 0) respectively with the horizontal, then their maximum heights are in the ratio **

**(a) 1 : 1 **

**(b) sin Î¸ : cos Î¸ **

**(c) sin**^{2} Î¸ : cos^{2 }Î¸

**(d) cos Î¸ : sin Î¸**

**Ans: **sin^{2} Î¸ : cos^{2 }Î¸

**Sol: **

Thus,

Option (c) is correct.

**Ques 5: A gun is firing bullets with velocity v**_{0} by rotating through 360Â° in the horizontal plane. The maximum area covered by the bullets is

**Ans: **

**Sol: **Equation to trajectory is

**Ques 6: A body is projected at an angle 60Â° with the horizontal with kinetic energy K. When the velocity makes an angle 30Â° with the horizontal, the kinetic energy of the body will be **

**(a) K/2 **

**(b) K/3 **

**(c) 2K/3 **

**(d) 3K/4**

**Ans: **K/3

**Sol: **v cos Ï† = u cos Î¸

or

or

âˆ´ Option (b) is correct.

**Ques 7: The range of a projectile at an angle 0 is equal to half of the maximum range if thrown at the same speed. The angle of projection 0 is given by **

**(a) 15Â° **

**(b) 30Â° **

**(c) 60Â° **

**(d) data insufficient**

**Ans: **15Â°

**Sol: **

or

or 2Î¸ = 30Â°

âˆ´ Î¸ = 15Â°

Option (a) is correct.

**Ques 8:** **If T**_{1} and T_{2} are the times of flight for two complementary angles, then the range of projectile R is given by

**Ans: **

**Sol: **

**âˆ´ **

**or **

**â‡’ **

Option (d) is correct.

**Ques 9: A grass hopper can jump maximum distance 1.6 m. It spends negligible time on ground. How far can it go in 10âˆš2 s. **

**(a) 45 m **

**(b) 30 m **

**(c) 20 m **

**(d) 40 m**

**Ans: **40 m

**Sol: **R_{max} = 1.6 m

â‡’ u = 4 m/s

âˆ´

= 25

âˆ´ Grass hopper would go = 25 x 1.6 m i.e., 40 m.

Option (d) is correct.

**Ques 10: Average velocity of a particle in projectile motion between its starting point and the highest point of its trajectory is (projection speed = u, angle of projection from horizontal = Î¸)**

**(a) u cos Î¸**

**Ans: **

**Sol: **

Option (b) is correct.

**Ques 11: A train is moving on a track at 30 ms**^{-1}. A ball is thrown from it perpendicular to the direction of motion at 30 ms^{-1} at 45Â° from horizontal. Find the distance of ball from the point of projection on train to the point where it strikes the ground.

**(a) 90 m **

**(b) 90 âˆš3 m **

**(c) 60 m **

**(d) 60 âˆš3 m**

**Ans: **90 m

**Sol: **

**âˆ´ **

Option (b) is correct.

**Ques 12: A body is projected at time t = 0 from a certain point on a planetâ€™s surface with a certain velocity at a certain angle with the planetâ€™s surface (assumed horizontal). The horizontal and vertical displacements x and y (in metre) respectively vary with time t in second as, x = (10âˆš3) 7 and y = 10t - t**^{2}. The m axim um height attained by the body is

**(a) 200 m **

**(b) 100 m **

**(c) 50 m **

**(d) 25 m**

**Ans: **25 m

**Sol: **At maximum height

dy/dt = 0

i.e.,

or 10 - 2t = 0

or t = 5 s

âˆ´ Maximum height attained = 10 (5) - 52

= 25 m

Option (d) is correct.

**Ques 13: A particle is fired horizontally from an inclined plane of inclination 30Â° with horizontal with speed 50 ms**^{-1}. If g = 10 ms^{-2}, the range measured along the incline is

**(a) 500 m**

**(b) **

**(c) **

**(d) **

**Ans: **

**Sol: **

As Î± = 0 (according to question)

Option (b) is correct.

**Ques 14: Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is Ï€/3 and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metres is**

**(a) 336 **

**(b) 224 **

**(c) 56 **

**(d) 34**** **

**Ans: **34

**Sol:** First particle:

H_{max} = 102 m

âˆ´

â‡’

Second particle:

Range of the second particle will be equal to that of particle

if,

sin 2Ï† = sin 3Î±

2Ï† = Ï€ - 2Î±

or

âˆ´ Maximum height attained by second particle

Option (d) is correct.

**Ques 15: A ball is projected upwards from the top of a tower with a velocity 50 ms**^{-1} making an angle 30Â° with the horizontal. The height of tower is 70 m. After how many seconds from the instant of throwing, will the ball reach the ground, (g = 10 ms^{-2})

**(a) 2 s **

**(b) 5 s **

**(c) 7 s **

**(d) 9 s**

**Ans: **7 s

**Sol: **

**âˆ´ **

or 5t^{2} - 25t - 70 = 0

or t^{2} - 5t - 14 = 0

(t - 7) (t + 2) = 0

t = 7 s

(- 2 s not possible)

Option (c) is correct.

**Ques 16: A fixed mortar fires a bomb at an angle of 53Â° above the horizontal with a muzzle velocity of 80 ms**^{-1}. A tank is advancing directly towards the mortar on level ground at a constant speed of 5m/s. The initial separation (at the instant mortar is fired) between the mortar and tank, so that the tank would be hit is [Take g = 10 ms^{-2}]

**(a) 662.4 m **

**(b) 526.3 m **

**(c) 486.6 m **

**(d) None of these**

**Sol: **Initial separation

Option (d) is correct.