Physics-
General
Easy

Question

The relationship between force and position is shown in the figure given (in one dimensional case) calculate the work done by the force in displacing a body from x=0 cm to x=5 cm

  1. 30 ergs    
  2. 70 ergs    
  3. 20 ergs    
  4. 60 ergs    

The correct answer is: 30 ergs

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physics-General
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equals 3 to the power of 2 end exponent plus 4 to the power of 2 end exponent minus 2 cross times 3 cross times 4 cos60 degree
equals 13
A B equals square root of 13
General
physics-

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T sin invisible function application theta equals M omega to the power of 2 end exponent R(i)
T sin invisible function application theta equals M omega to the power of 2 end exponent L sin invisible function application theta(ii)
From (i) and (ii)
T equals M omega to the power of 2 end exponent L
equals M blank 4 pi to the power of 2 end exponent n to the power of 2 end exponent L
equals M blank 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L equals 16 blank M L

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physics-General
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T sin invisible function application theta equals M omega to the power of 2 end exponent L sin invisible function application theta(ii)
From (i) and (ii)
T equals M omega to the power of 2 end exponent L
equals M blank 4 pi to the power of 2 end exponent n to the power of 2 end exponent L
equals M blank 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L equals 16 blank M L
General
physics-

A piece of wire is bent in the shape of a parabola y equals k x to the power of 2 end exponent blank left parenthesis y-axis vertical) with a bead of mass m on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

m a cos invisible function application theta equals m g cos invisible function application left parenthesis 90 minus theta right parenthesis
rightwards double arrow fraction numerator a over denominator g end fraction equals tan invisible function application theta rightwards double arrow fraction numerator a over denominator g end fraction equals fraction numerator d y over denominator d x end fraction
rightwards double arrow fraction numerator d over denominator d x end fraction open parentheses k x close parentheses to the power of 2 end exponent equals fraction numerator a over denominator g end fraction rightwards double arrow x equals fraction numerator a over denominator 2 g k end fraction

A piece of wire is bent in the shape of a parabola y equals k x to the power of 2 end exponent blank left parenthesis y-axis vertical) with a bead of mass m on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

physics-General
m a cos invisible function application theta equals m g cos invisible function application left parenthesis 90 minus theta right parenthesis
rightwards double arrow fraction numerator a over denominator g end fraction equals tan invisible function application theta rightwards double arrow fraction numerator a over denominator g end fraction equals fraction numerator d y over denominator d x end fraction
rightwards double arrow fraction numerator d over denominator d x end fraction open parentheses k x close parentheses to the power of 2 end exponent equals fraction numerator a over denominator g end fraction rightwards double arrow x equals fraction numerator a over denominator 2 g k end fraction