If an object is placed at the center of curvature of a concave mirror, the image formed is: MCQ with Answer and Explanation

If an object is placed at the center of curvature of a concave mirror, the image formed is:
A. Virtual, erect, and diminished.
B. Virtual, erect, and magnified.
C. Real, inverted, and of the same size.
D. Real, inverted, and magnified.
Answer: Option C
Solution (By JKExamLibrary)
For a concave mirror, when an object is placed exactly at the center of curvature (C), the image is also formed at C. The image is real (can be captured on a screen), inverted (upside down), and exactly the same size as the object. Magnification in this specific case is exactly -1.

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Question #1
Two slabs of equal thickness and cross-sectional area have thermal conductivities K1 and K2. If they are joined in series, the equivalent thermal conductivity of the combination is:
A. 2K1 * K2 / (K1 + K2)
B. sqrt(K1^2 + K2^2)
C. K1 * K2 / (K1 + K2)
D. (K1 + K2) / 2

Correct Answer: Option A


Explanation:
For slabs in series, the rate of heat flow (H) is the same. Total resistance R_eq = R1 + R2. Since thermal resistance R = L / (KA), and total length is 2L: (2L) / (K_eq * A) = (L / K1A) + (L / K2A). Canceling L/A yields 2/K_eq = 1/K1 + 1/K2. Solving gives K_eq = 2K1K2 / (K1 + K2).

This question belongs to: Science Physics
Question #2
Which of the following operates strictly on the principle of conservation of linear momentum?
A. Rocket
B. Hovercraft
C. Aeroplane
D. Helicopter

Correct Answer: Option A


Explanation:
A rocket works on the principle of conservation of linear momentum. As the exhaust gases are expelled downward at high velocity, they carry downward momentum. To conserve the total momentum of the system (which is initially zero), the rocket must acquire an equal and opposite (upward) momentum, propelling it forward.

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Question #3
At what depth below the surface of the Earth does the acceleration due to gravity become zero?
A. At the center of the Earth
B. It never becomes zero
C. At a depth equal to half the radius of the Earth
D. At a depth equal to one-fourth the radius of the Earth

Correct Answer: Option A


Explanation:
The acceleration due to gravity at a depth 'd' is given by g' = g(1 - d/R), where R is the radius of the Earth. If we go to the center of the Earth, the depth 'd' becomes exactly equal to R. Substituting d = R into the formula gives g' = g(1 - R/R) = g(1 - 1) = 0. So, gravity is zero at the core.

This question belongs to: Science Physics