If the radius of the earth shrinks by 1%, its mass remaining the same, the value of 'g' on the earth's surface would:
A. Increase by 2%
B. Increase by 1%
C. Decrease by 1%
D. Decrease by 2%
Answer: Option A
Solution (By JKSSB Mock Tests)
The acceleration due to gravity is given by g = GM/R². For a small change, taking the derivative or using error approximation: Δg/g = -2(ΔR/R). If R shrinks by 1% (ΔR/R = -1%), then Δg/g = -2(-1%) = +2%. Therefore, the value of 'g' will increase by approximately 2%.
Explanation:
Power P = 1/f (in meters). P = -2 D ⇒ f = 1/(-2) = -0.5 m = -50 cm. Negative focal length indicates diverging (concave) lens. Convex lenses have positive power. Option A correctly states concave lens with |f| = 50 cm. Memory tip: 'Negative power = concave lens; f(in cm) = 100/P(in D)'. This direct application of lens power definition is common in competitive exams. Always convert diopters to focal length carefully, noting sign convention: negative for diverging lenses, positive for converging.
Explanation:
Dimensionless quantities: angle (radian = arc/radius), strain (ΔL/L), refractive index (ratio of speeds). All have [M⁰L⁰T⁰]. Memory aid: 'Ratios of same dimensions ⇒ dimensionless'. Dimensional analysis question frequently tested in competitive exams to identify dimensionless physical quantities.
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