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Question

The frequency of a radar is 780 MHz. After getting reflected from an approaching aeroplane, the apparent frequency is more than the actual frequency by 2.6 kHz. The aeroplane has a speed of

A
2 km/s
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B
1 km/s
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C
0.5 km/s
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D
0.25 km/s
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Solution

The correct option is C 0.5 km/s
f=(c+vacva)f
where c is the velocity of the radio wave, an electro-magnetic wave, i.e., \(c = 3 \times 10^8 m/s\) and vs is velocity of aeroplane.
ff=[c+vacva1]fΔf=2vafcva
Since approaching aeroplane cannot have a speed comparable to the speed of electromagnetic wave,
so vs << c.
Δf=2vafc2.6103=2vA(780×106)3×108VA=0.5×103m/s=0.5km/s

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