Question

A body has an acceleration of $10km/{h^2}$. Find its value in CGS system
(A) $0.0772 cm/{\sec ^2}$
(B) $0.00772 cm/{\sec ^2}$
(C) $0.772 cm/{\sec ^2}$
(D) $0.000772 cm/{\sec ^2}$

Answer 1

Acceleration is given in kilometers and hour, convert them to their respective CGS units and then calculate the value of acceleration in the CGS unit.

Complete step by step answer:
The CGS system has a full form of centimeter gram second. centimeter is the CGS unit of length, gram is the CGS unit of mass, and 2nd is the CGS unit of time. We must convert the acceleration of the body given in kilometer per hour square to its CGS unit that will be centimeter per second square.
Now for the conversion first we need to convert kilometer into centimeter. We know that one-kilometer equals 1000 meters, and one meter is equal to 100 centimeters. Therefore, one kilometer in centimeters will be
$1km = 1000m$
$1m = 100cm$
$1km = 1000m = 1000 \times 100cm = {10^5}cm$
Now we must convert hours to seconds. We know that one hour equals to 60 minutes, and one-minute equals to 60 seconds. Therefore, one hour to seconds will be
$1h = 60\min$
$1\min = 60\sec$
$1h = 60\min = 60 \times 60\sec = 3600\sec$
Now since we have converted both kilometers and hours into their respective CGS units, we must now calculate the CGS unit for the acceleration.
$a = 10km/{h^2} = \dfrac{{10km}}{{1{h^2}}} \\\ a = \dfrac{{10 \times {{10}^5}cm}}{{3600 \times 3600{{\sec }^2}}} = 0.0772cm/{\sec ^2} \\\$
Hence, option(A) is the correct answer.**

Note: While converting the units into their respective CGS units, solve the equations carefully as there could be a high chance of calculation errors.