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

Subtopic:  Relative Motion |
 60%
From NCERT
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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° east of the south. The resultant velocity of the boat is:

1. 12 km/h at 23.4ο east of west

2. 22 km/h at 23.4ο north of east

3. 22 km/h at 23.4ο east of north

4. 20 km/h at 23.4ο north of wast

Subtopic:  Relative Motion |
From NCERT
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The position of a particle is given by;
\(\overrightarrow{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m 
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\overrightarrow{v}(t)\) at \(t=1.0\) s are:

1. \(4\) m/s \(53^\circ\) with \(x\)-axis
2. \(4\) m/s \(37^\circ\) with \(x\)-axis
3. \(5\) m/s \(53^\circ\) with \(y\)-axis
4. \(5\) m/s \(53^\circ\) with \(x\)-axis
Subtopic:  Speed & Velocity |
 66%
From NCERT
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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
Subtopic:  Uniformly Accelerated Motion |
 70%
From NCERT
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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.
Subtopic:  Relative Motion |
 56%
From NCERT
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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.

Subtopic:  Projectile Motion |
 79%
From NCERT
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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

Subtopic:  Projectile Motion |
 70%
From NCERT
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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

Subtopic:  Projectile Motion |
 85%
From NCERT
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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

Subtopic:  Circular Motion |
 69%
From NCERT
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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. \(\mathrm{yes},\) \(2.3~\mathrm{cm/s^2}\)
2. \(\mathrm{no},\) \(5.3~\mathrm{cm/s^2}\)
3. \(\mathrm{yes},\) \(5.3~\mathrm{cm/s^2}\)
4. \(\mathrm{no},\) \(2.3~\mathrm{cm/s^2}\)

Subtopic:  Circular Motion |
From NCERT
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