General
✓✗Two forces of 5 N and 12 N act at a point at right angles. The angle the resultant makes with the 12 N force is
- 45°
- \( \tan^{-1}\left(\dfrac{12}{5}\right) \)
- \( \tan^{-1}\left(\dfrac{5}{12}\right) \)
- \( \sin^{-1}\left(\dfrac{5}{12}\right) \)
General
✓✗A particle has velocity \( \vec{v} = 2\hat{i} + 3\hat{j} \) m/s at t = 0 and a constant acceleration \( -\hat{j} \) m s−2. At what time is its velocity parallel to the x-axis?
- 6 s
- 1.5 s
- 3 s
- 2 s
General
✓✗A ball rolls off the edge of a horizontal table 1.25 m high and lands 2 m from the foot of the table. Its speed on leaving the table was (take g = 10 m s−2)
- 8 m/s
- 4 m/s
- 2 m/s
- 5 m/s
General
✓✗A particle moves in a circle of radius 5 cm with constant speed and a time period of \( 0.2\pi \) s. The acceleration of the particle is
- 25 m s−2
- 36 m s−2
- 15 m s−2
- 5 m s−2
General
✓✗A particle moves with velocity \( \vec{v} = 2t\,\hat{i} + 3\hat{j} \) m/s starting from the origin. The equation of its path is
- \( y = 3x \)
- \( x^2 + y^2 = 9 \)
- \( x = \dfrac{y^2}{9} \)
- \( y = \dfrac{x^2}{9} \)
General
✓✗Two particles A and B move in circles of radii 2 m and 4 m with the same speed. The ratio of their centripetal accelerations is
- 2 : 1
- 1 : 4
- 1 : 2
- 4 : 1
General
✓✗A force of 20 N acts at 60° to the horizontal. Its horizontal component is
- 10 N
- 17.3 N
- \( 10\sqrt{3} \) N
- 20 N
General
✓✗The time of flight of a projectile depends on
- the horizontal component only
- the range only
- the vertical component of the initial velocity
- the mass of the projectile
General
✓✗Which of the following quantities is NOT a vector?
- Momentum
- Angular velocity
- Weight
- Electric current
General
✓✗A cricket ball is thrown with a speed of 28 m/s in a direction 30° above the horizontal. The time taken to return to the same level is (g = 9.8 m s−2)
- 5.72 s
- 2.86 s
- 4 s
- 1.43 s
General
✓✗A particle moves with velocity \( \vec{v} = 2\hat{i} - 4\hat{j} \) m/s for 3 s. Its displacement is
- \( 6\hat{i} + 12\hat{j} \) m
- \( 2\hat{i} - 4\hat{j} \) m
- \( \dfrac{2}{3}\hat{i} - \dfrac{4}{3}\hat{j} \) m
- \( 6\hat{i} - 12\hat{j} \) m
General
✓✗The equation of the trajectory of a projectile is \( y = \sqrt{3}\,x - \dfrac{g x^2}{2} \) (SI units). The angle of projection is
- \( \tan^{-1}\left(\dfrac{1}{\sqrt3}\right) \)
- 45°
- 60°
- 30°
General
✓✗A bomber flying horizontally at 720 km/h at a height of 2 km wants to hit a target on the ground. At what horizontal distance before the target must it release the bomb? (take g = 10 m s−2)
- 1 km
- 2 km
- 8 km
- 4 km
General
✓✗Identify the vector quantity among the following.
- energy
- distance
- angular momentum
- heat
General
✓✗The scalar product of two perpendicular vectors is
- negative
- the product of their magnitudes
- maximum
- zero