Q. No.Rain is falling vertically with a speed of \(35~\text{ms}^{-1}\). Winds starts blowing after sometime with a speed of \(12~\text{ms}^{-1}\) in east to west direction. At what angle should a boy waiting at a bus stop hold his umbrella?
| 1. | \(16^{\circ}\) with the vertical |
| 2. | \(15^{\circ}\) with the vertical |
| 3. | \(19^{\circ}\) with the vertical |
| 4. | \(19^{\circ}\) with the horizontal |
A motorboat is racing towards the north at \(25\) km/h and the water current in that region is \(10\) km/h in the direction of \(60^\circ\) east of the south. The resultant velocity of the boat is:
| 1. | \(12\) km/h at \(23 . 4^\circ\) east of west |
| 2. | \(22\) km/h at \(23 . 4^\circ\) north of east |
| 3. | \(22\) km/h at \(23 . 4^\circ\) east of north |
| 4. | \(20\) km/h at \(23 . 4^\circ\) north of west |
1. \(4~\text{m/s},\) \(53^\circ\) with \(x\)-axis
2. \(4~\text{m/s},\) \(37^\circ\) with \(x\)-axis
3. \(5~\text{m/s},\) \(53^\circ\) with \(y\)-axis
4. \(5~\text{m/s},\) \(53^\circ\) with \(x\)-axis
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2\). What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84\) m?
| 1. | \(36\) m/s | 2. | \(26\) m/s |
| 3. | \(1\) m/s | 4. | \(0\) m/s |
Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?
| 1. | in the vertical direction only. |
| 2. | \(19^\circ\) with vertical towards east. |
| 3. | \(19^\circ\) with vertical towards the west. |
| 4. | \(19^\circ\) with vertical towards the south. |
Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:
| 1. | are equal to each other. |
| 2. | are not equal to each other. |
| 3. | are sometimes equal and sometimes not equal to each other. |
| 4. | depends on the difference between the angles. |
A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))
| 1. | \(10\) s and \(99\) m/s |
| 2. | \(10\) s and \(15\) m/s |
| 3. | \(5\) s and \(99\) m/s |
| 4. | \(5\) s and \(15\) m/s |
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:
1. \(2.5\) s
2. \(2.9\) s
3. \(3.5\) s
4. \(3\) s
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?
| 1. | \(0.62\) rad/s | 2. | \(0.06\) rad/s |
| 3. | \(4.40\) rad/s | 4. | \(0.44\) rad/s |
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?
1. \(\text{yes},\) \(2.3~\text{cm/s}^2\)
2. \(\text{no},\) \(5.3~\text{cm/s}^2\)
3. \(\text{yes},\) \(5.3~\text{cm/s}^2\)
4. \(\text{no},\) \(2.3~\text{cm/s}^2\)
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