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Why is it advised to tie any luggage kept on the roof of a bus with a rope?
 
In moving vehicle like bus, the motion is , the speed of vehicle  and it may apply brake suddenly or takes sudden turn.
 
When some luggage is placed on the roof of a bus which is initially at rest, the acceleration of the bus in the  will exert a force in the on the luggage.
 
In a similar manner, when a bus which is initially in a state of motion suddenly comes to rest due to the application of brakes, a force in the  is exerted on the luggage.
 
Depending on the  of the luggage and the  of the force, the luggage may fall off the bus due to .
 
So, tying up the luggage will secure its position and prevent it from falling off the bus.