In the figure, the coefficient of friction between the floor and body $$B$$ is $$0.1.$$ The coefficient of friction between bodies $$B$$ and $$A$$ is $$0.2.$$ A force $$F$$ is applied as shown on $$B.$$ The mass of $$A$$ is $$rn/2$$ and of $$B$$ is $$m.$$

 (a) The bodies will move together if $$F = 0.25\text{mg}$$ (b) The $$A$$ will slip with $$B$$ if $$F = 0.5\text{mg}$$ (c) The bodies will move together if $$F = 0.5\text{mg}$$ (d) The bodies will be at rest if $$F = 0.1\text{mg}$$ (e) The maximum value of $$F$$ for which the two bodies will move together is $$0.45\text{mg}$$

Which of the following statement(s) is/are true?
1. (a), (b), (d), (e)
2. (a), (c), (d), (e)
3. (b), (c), (d)
4. (a), (b), (c)

Subtopic: Â Application of Laws |Â Friction |
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The figure shows the position-time graph of a particle of mass $$4~\text{kg}$$. What is the force on the particle for $$t>4~\text{s}$$
(Consider one-dimensional motion only).

 1 $$0$$ 2 $$40~\text{N}$$ 3 $$20~\text{N}$$ 4 $$10~\text{N}$$
Subtopic: Â Application of Laws |
Â 81%
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Given below are two statements:
 Assertion (A): A man who falls from a height on a cement floor receives more injury than when he falls from the same height on a heap of sand. Reason (R): The impulse applied by a cement floor is less than the impulse applied by a sand floor.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.

Subtopic: Â Application of Laws |
Â 66%
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Given below are two statements:
 Assertion (A): A rocket moves forward by pushing the surrounding air backward. Reason (R): It derives the necessary thrust to move forward according to Newton's first law of motion.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.

Subtopic: Â Application of Laws |
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Given below are two statements:
 Assertion (A): A rocket works on the principle of conservation of linear momentum. Reason (R): Higher is the velocity, smaller is the pressure and vice-versa.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.

Subtopic: Â Application of Laws |
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Given below are two statements:
 Assertion (A): The driver in a vehicle moving at a constant speed on a straight road is in a non-inertial frame of reference. Reason (R): A reference frame in which Newton's law of motion is applicable is non-inertial.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.

Subtopic: Â Application of Laws |
Â 58%
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Given below are two statements:
 Assertion (A): A man in a closed cabin, which is falling freely, does not experience gravity. Reason (R): Inertial and gravitational mass have equivalence.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.
Subtopic: Â Application of Laws |
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Given below are two statements:
 Assertion (A): The principle of rocket propulsion is a special case of a variable mass system. Reason (R): The principle of rocket propulsion can be explained by Newton's second law.

 1 Both (A) and (R) are true and (R) is the correct explanation of (A). 2 Both (A) and (R) are true but (R) is not the correct explanation of (A). 3 (A) is true but (R) is false. 4 Both (A) and (R) are false.

Subtopic: Â Application of Laws |
Â 56%
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