(C) Let $d$ be the distance of the epicenter from the seismograph.The time taken by $P$ waves is $t_p = \frac{d}{V_p} = \frac{d}{8.0} \, s$.The time t

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(C) Let $d$ be the distance of the epicenter from the seismograph.The time taken by $P$ waves is $t_p = \frac{d}{V_p} = \frac{d}{8.0} \, s$.The time taken by $S$ waves is $t_s = \frac{d}{V_s} = \frac{d}{4.5} \, s$.Given that the $P$ wave arrives $4.0 \, min$ before the $S$ wave,we have $t_s - t_p = 4.0 \, min = 240 \, s$.Substituting the values: $\frac{d}{4.5} - \frac{d}{8.0} = 240$.Taking $d$ as common: $d \left( \frac{8.0 - 4.5}{4.5 \times 8.0} \right) = 240$.$d \left( \frac{3.5}{36} \right) = 240$.$d = \frac{240 \times 36}{3.5} \approx 2468.57 \, km$.Rounding to the nearest given option,$d \approx 2500 \, km$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about ..... $km$.

AIIMS 2003 All AIIMS

A
$25$
B
$250$
C
$2500$
D
$5000$

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The ratio of the de-Broglie wavelength of an $\alpha$-particle to that of a proton,when both are subjected to the same magnetic field such that the radii of their paths are equal,assuming the magnetic field induction vector $\overrightarrow{B}$ is perpendicular to the velocity vectors of both particles,is:

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Energy required to remove an electron from an aluminium surface is $4.2 \text{ eV}$. If light of wavelength $2000 \text{ \AA}$ falls on the surface, the velocity of the fastest electron ejected from the surface will be:

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The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:
$I$. $f$ is one-one
$II$. $f$ is onto
$III$. $f$ is a decreasing function
Which of these statements are true?