Rope and Brain
In the above you can see a rope whose mass is given by the equation
2M^2*(x)
, where M = 1 kg, and x is the distance from point
A
. Find the tension at the string on:-
(1.) Point
B
(2. ) Point
D
, but for this case x is the distance from point
B
, and below point
B
the mass of the whole string is given by
2M^2
.
(TAKE g to be 10ms^-2)
Find Z+ Y ( where Z is the answer for first part and Y for the second one). ( In your final answer which you choose from the options given, dont include 'N')
NOTE : POINT D IS THE BASE NOT POINT A . THE PICTURE IS INVERTED. SORRY FOR THE INCONVENIENCE
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1 solution
we can see that the mass of the string here, depends upon x. so we can write:- dm/dx [which means mass of a small piece of thread w.r.t to x )= 2M^2*( x )
=> dm = [2M^2*( x )]dx
integrating this equation, we get m=M^2*( x^2 ) ..............(1)
hence taking out the mass on point B , we use the above the above equation. (where x =1, and M is constant =1 kg)
we get, => m = (1^2)(1^2)=1
as tension is force, and we know F=ma
we infer tension = (1) *g = 10N
For the second part we know =>
{the mass of string from ( A to B ) + mass of string from ( D _ to _C )}* g = Tension
we know mass of string A to B is given by 2M^2= 2(1kg)=2kg
(NOTE: But here x is the distance from B not A )
so we get => m( DB )= (M^2)*( x )^2
hence we conclude total mass for part 2 is (4+2)kg =6kg
therefore tension = mg
=> T = (6)(10)N = 60 N
As the question asked the sum of the answers of the two parts, our final fnal answer comes out to be :-
60N + 10N =70N
plus we are also told to exclude 'N' in our final answer. Therefore the correct option is 70.