The range of a bullet fired from a gun at an angle π4 - ϕ with the horizontal is the same as the range of another bullet fired from that gun at an angle θ with the horizontal. Then,

1.  θ = ϕ

2.  θ = π4

3.  θ = π4 + ϕ

4.  θ = ϕ - π4

Subtopic:  Projectile Motion |
 72%
From NCERT
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A boy runs on a circular track of radius \(\mathrm{R}\) (in km) with a speed of πR2 km/h in the clockwise direction for \(3\)and then with πR km/h in the anticlockwise direction for \(1\) h. The magnitude of his displacement will be: 
1.  πR2

2.  R2

3.  3πR2

4.  2R

Subtopic:  Position & Displacement |
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Two projectiles P and Q are projected with the same speed at angles 60° and 30° with horizontal on level ground, then: [R = Range, T = Time of flight, H = Maximum height]

(1) RP=2RQ

(2) TP=3 TQ

(3) H=3HP

(4) All of these

Subtopic:  Projectile Motion |
 62%
From NCERT
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A body is projected with the same speed at two different angles covers the same horizontal distance R. If T1 and T2 are two times of flights, then R is equal to :

1.  gT1T22

2.  2gT1T2

3.  12gT1T2T1 + T2

4.  2gT1T2

Subtopic:  Projectile Motion |
 70%
From NCERT
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A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by r = 2ti^ + 3t2j^. The equation of the trajectory of the body is:

1. y = 1.5 x

2. y = 0.75 x2

3. y = 1.5 x2

4. y = 0.45 x2

Subtopic:  Position & Displacement |
 66%
From NCERT
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A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m

Subtopic:  Uniformly Accelerated Motion |
 65%
From NCERT
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A particle is revolving in a circular path of radius 200 m at a speed of 20 m/s. Its speed is increasing at a rate of 5 m/s2. Its acceleration is :

(1) 2 m/s2

(2) 7 m/s2

(3) 3 m/s2

(4) 5 m/s2

Subtopic:  Circular Motion |
 68%
From NCERT
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The ratio of maximum height attained by two projectiles of the same mass is 25: 9. The ratio of their minimum kinetic energy is 4: 9. The ratio of their ranges is:

(1) 25: 4

(2) 10: 9

(3) 5: 2

(4) 1: 1

Subtopic:  Projectile Motion |
 64%
From NCERT
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If a particle is moving in a circular orbit with constant speed, then:

1. its velocity is variable.
2. its acceleration is variable.
3. its angular momentum is constant.
4. All of the above

Subtopic:  Circular Motion |
 77%
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In a uniform circular motion,

(1) Both velocity and acceleration are constant.

(2) Acceleration and speed are constant but velocity changes.

(3) Both acceleration and velocity change.

(4) Both acceleration and speed are constant.

Subtopic:  Circular Motion |
 64%
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