# 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 $23.{4}^{ο}$ east of west

2. 22 km/h at $23.{4}^{ο}$ north of east

3. 22 km/h at $23.{4}^{ο}$ east of north

4. 20 km/h at $23.{4}^{ο}$ 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 $\stackrel{}{\mathrm{}}$
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%
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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%
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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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