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Chapter 3: Problem 369

which of the following statement is correct? (A) A body has a constant velocity but a varying speed. (B) A body has a constant speed but a varying value of acceleration. (C) A body has a constant speed and zero acceleration. (D) A body has a constant speed but velocity is zero.

Short Answer

Expert verified
The correct statements are: (B) A body has a constant speed but a varying value of acceleration, and (C) A body has a constant speed and zero acceleration.

Step by step solution

01

Statement A: A body has a constant velocity but a varying speed.

Velocity is a vector quantity, which means it has both magnitude (speed) and direction. If a body has constant velocity, it means both its speed and direction remain unchanged. Varying speed and a constant velocity contradict each other, so statement A is incorrect.
02

Statement B: A body has a constant speed but a varying value of acceleration.

A body can have a constant speed while still undergoing a centripetal acceleration if it is moving in a circular path. The speed remains the same, but the direction changes continuously in circular motion. Since acceleration is related to change in velocity, varying acceleration is possible even with constant speed. Statement B is correct.
03

Statement C: A body has a constant speed and zero acceleration.

A body moving with constant speed can have zero acceleration, only if it is moving in a straight line and not changing direction. In this case, there is no variation in its motion, both in terms of speed and direction. This statement is ~~incorrect~~ correct, but it is not the only correct statement. Note: The original answer said that Statement C is incorrect. Upon review, I believe that Statement C is actually correct based on the analysis provided. Therefore, there are two correct statements in this exercise, B and C.
04

Statement D: A body has a constant speed but velocity is zero.

Speed is a scalar quantity, which is the magnitude of velocity. A constant speed implies that the body is always moving. If the velocity is zero, it means the body is at rest, and its speed should also be zero. This statement is contradictory; hence, statement D is incorrect. In conclusion:
05

The correct statements are:

(B) A body has a constant speed but a varying value of acceleration, and (C) A body has a constant speed and zero acceleration.

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Most popular questions from this chapter

A stone of mass \(2 \mathrm{~kg}\) is tied to a string of length $0.5 \mathrm{~m}\( It the breaking tension of the string is \)900 \mathrm{~N}$, then the maximum angular velocity the stone can have in uniform circular motion is (A) \(30 \mathrm{rad} / \mathrm{s}\) (B) \(20 \mathrm{rad} / \mathrm{s}\) (C) \(10 \mathrm{rad} / \mathrm{s}\) (D) \(25 \mathrm{rad} / \mathrm{s}\)

A plate of mass \(\mathrm{M}\) is placed on a horizontal frictionless surface and a body of mass \(m\) is placed on this plate, The coefficient of dynamic friction between this body and the plate is \(\mu\). If a force $2 \mu \mathrm{mg}\(. is applied to the body of mass \)\mathrm{m}$ along the horizontal direction the acceleration of the plate will be (A) \((\mu \mathrm{m} / \mathrm{M}) \mathrm{g}\) (B) \([\mu \mathrm{m} /(\mathrm{M}+\mathrm{m})] \mathrm{g}\) (C) \([(2 \mu \mathrm{m}) / \mathrm{M}] \mathrm{g}\) (D) \([(2 \mu \mathrm{m}) /(\mathrm{M}+\mathrm{m})] \mathrm{g}\)

Two masses \(\mathrm{M}\) and \((\mathrm{M} / 2)\) are joined together by means of light inextensible string passed over a frictionless pulley as shown in fig. When the bigger mass is released, the small one will ascend with an acceleration (A) \((\mathrm{g} / 3)\) (B) \((3 \mathrm{~g} / 2)\) (C) \(\mathrm{g}\) (D) \((\mathrm{g} / 2)\)

Force of \(5 \mathrm{~N}\) acts on a body of weight \(9.8 \mathrm{~N}\). what is the acceleration produced in \(\mathrm{ms}^{-2}\). (A) \(49.00\) (B) \(5.00\) (C) \(1.46\) (D) \(0.51\)

Same force acts on two bodies of different masses \(2 \mathrm{~kg}\) and $4 \mathrm{~kg}$ initially at rest. the ratio of times required to acquire same final velocity is (A) \(2: 1\) (B) \(1: 2\) (C) \(1: 1\) (D) \(4: 16\)
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