A body starts from rest and moves with uniform acceleration a. The ratio of distances covered in the 1st, 2nd, and 3rd seconds of motion is: MCQ with Answer and Explanation
A body starts from rest and moves with uniform acceleration a. The ratio of distances covered in the 1st, 2nd, and 3rd seconds of motion is:
A. 1:4:9
B. 1:2:3
C. 1:3:5
D. 1:1:1
Answer: Option C
Solution (By JKSSB Mock Tests)
Distance covered in nth second: sₙ = u + a(2n-1)/2. With u=0, sₙ ∝ (2n-1). For n=1: 2(1)-1=1; n=2: 3; n=3:5. Thus ratio 1:3:5. This result holds for any uniformly accelerated motion starting from rest. The distances covered in successive equal time intervals follow odd number ratio. Memory aid: This is a standard result derivable from s = ut + ½at² by calculating s at t=n and t=n-1. Frequently appears in competitive exams testing equation of motion applications.
Explanation:
An isochoric process is a thermodynamic process in which the volume of the closed system remains constant (delta V = 0). Because there is no change in volume, the system does zero pressure-volume work (W = Pdelta V = 0). According to the first law of thermodynamics, any heat added goes entirely into increasing the internal energy. Isobaric is constant pressure; isothermal is constant temperature.
Explanation:
Damping opposes the motion of an oscillator (like a pendulum in thick oil). In 'underdamped' systems, it oscillates with decaying amplitude. In 'critically damped' systems, it returns to equilibrium as fast as possible without oscillating. In 'overdamped' or heavily damped systems, the resistive force is so strong that it slowly creeps back to equilibrium without ever crossing it to oscillate.
Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.
A.Both A and R are true but R is NOT the correct explanation of A.
B.A is true but R is false.
C.A is false but R is true.
D.Both A and R are true and R is the correct explanation of A.
Explanation:
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.
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