Question

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$. (b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1 .$ (c) Statement $-1$ is true, statement $-2$ is false (d) Statement $-1$ is false, statement $-2$ is true (A) $a$ (B) $b$ (C) $\mathrm{c}$ (D) $\mathrm{d}$ Statement $-1:$ The periodic time of a stiff spring is less than that of a soft spring. Statement $-2:$ The periodic time of a spring depends on its force constant value and for a stiff spring, it is more. (A) a (B) $b$ (C) $\mathrm{c}$ (D) $\mathrm{d}$

Name: Problem 1412, Chapter 10: JEE Physics
Uploaded: 2021-10-10T16:11:01-08:00
Duration: 1 min 28 s
Channel: Supratim Pal

   For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1 .$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) $a$
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ The periodic time of a stiff spring is less than that of a soft spring. Statement $-2:$ The periodic time of a spring depends on its force constant value and for a stiff spring, it is more.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

JEE Physics

StemEZ 1st Edition

Chapter 10, Problem 1412

Instant Answer

Solved by Expert Supratim Pal

10/10/2021

Step 1

The first statement says that the periodic time of a stiff spring is less than that of a soft spring. The second statement says that the periodic time of a spring depends on its force constant value and for a stiff spring, it is more. Show more…

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For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$. (b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1 .$ (c) Statement $-1$ is true, statement $-2$ is false (d) Statement $-1$ is false, statement $-2$ is true (A) $a$ (B) $b$ (C) $\mathrm{c}$ (D) $\mathrm{d}$ Statement $-1:$ The periodic time of a stiff spring is less than that of a soft spring. Statement $-2:$ The periodic time of a spring depends on its force constant value and for a stiff spring, it is more. (A) a (B) $b$ (C) $\mathrm{c}$ (D) $\mathrm{d}$

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Key Concepts

Simple Harmonic Motion

This concept deals with systems that oscillate about an equilibrium position where the restoring force is directly proportional to the displacement from that equilibrium. It provides the framework within which many oscillatory phenomena, including mass-spring systems, are analyzed and understood.

Spring Constant

This refers to a measure of the stiffness of a spring, representing the force required to produce a unit change in length. A higher spring constant indicates a stiffer spring, and it plays a crucial role in determining how a system behaves under oscillatory motion.

Period Dependence on Mass and Spring Constant

In an oscillatory system like a mass attached to a spring, the period of oscillation is determined by the mass and the spring constant, following the relationship T = 2??(m/k). This equation shows that for a given mass, a stiffer spring (with a larger spring constant) leads to a shorter period, indicating faster oscillations.

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