General
✓✗The minimum resultant of two vectors of magnitudes 6 and 8 units is
- 14 units
- 10 units
- zero
- 2 units
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
✓✗In uniform circular motion of radius r and angular speed ω, the acceleration vector can be written as
- \( \vec{a} = \vec{0} \)
- \( \vec{a} = \omega^2\vec{r} \)
- \( \vec{a} = \omega\vec{r} \)
- \( \vec{a} = -\omega^2\vec{r} \)
General
✓✗Two particles A and B start from the origin simultaneously with velocities \( \vec{v}_A = 3\hat{i} \) m/s and \( \vec{v}_B = 4\hat{j} \) m/s (constant). The rate at which the distance between them increases is
- 12 m/s
- 7 m/s
- 5 m/s
- 1 m/s
General
✓✗In the previous situation (bomb from an aeroplane at 200 m/s, 500 m high), where is the aeroplane when the bomb hits the ground?
- 2000 m ahead of the point of impact
- 1000 m ahead
- 2000 m behind the point of impact
- vertically above the point of impact
General
✓✗A ball is thrown from the ground with velocity \( (10\hat{i} + 20\hat{j}) \) m/s, where \( \hat{j} \) is vertically up. Its horizontal range is (take g = 10 m s−2)
- 100 m
- 80 m
- 40 m
- 20 m
General
✓✗An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of a blade is
- 47.4 m s−2
- 1600 m s−2
- 50.55 m s−2
- 23.7 m s−2
General
✓✗A projectile has a time of flight of 4 s. Its maximum height is (take g = 10 m s−2)
- 40 m
- 20 m
- 80 m
- 10 m
General
✓✗A boat crosses a river heading perpendicular to the flow (see figure). The time to cross depends on
- the river width and the boat’s speed relative to water
- the drift only
- both speeds and the drift
- the river’s speed only
General
✓✗If the speed of a particle in uniform circular motion is doubled and the radius is halved, the centripetal acceleration becomes
- 4 times
- 2 times
- 8 times
- unchanged
General
✓✗A man walks 4 m east and then 3 m north. His resultant displacement makes an angle with east given by
- \( \tan^{-1}\left(\dfrac{3}{4}\right) \)
- \( \tan^{-1}\left(\dfrac{4}{3}\right) \)
- 45°
- 90°
General
✓✗A particle moves in a circle with uniform speed v. The magnitude of the change in velocity when it moves through 60° is
- \( \sqrt{3}v \)
- v
- 2v
- zero
General
✓✗If a unit vector is represented by \( 0.5\hat{i} - 0.8\hat{j} + c\hat{k} \), then the value of c is
- \( \sqrt{0.11} \)
- 1
- \( \sqrt{0.39} \)
- \( \sqrt{0.01} \)
General
✓✗A boat is sent across a river with a velocity of 8 km h−1. If the resultant velocity of the boat is 10 km h−1, then the velocity of the river is
- 6 km h−1
- 10 km h−1
- 12.8 km h−1
- 8 km h−1
General
✓✗The position vector of a particle is \( \vec{r} = 3t\,\hat{i} + 4t\,\hat{j} \) m. Its speed is
- 12 m/s
- 1 m/s
- 7 m/s
- 5 m/s