Question 1:
moderateA particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at x = 0, Work Done from x=0 to x = 12 m is:
Area bounded by force time graph represents work done so,Â
Work= ½(12+4)×10= 80 J
Question 2:
moderateA chord is used to lower vertically a block of mass M a distance d at a constant downward acceleration of g/4. Then the work done by the cord on the block is :
Forces acting on the object are , mg in downward direction and Tension force T in upward direction, as the object moves downward.
mg - T= ma= mg/4
so, T= 3mg/4
Work done by tension force is W= T.d.cos (180°)= -3mgd/4
Question 3:
moderateAn object of mass m is tied to string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases (it is pulled extremely slowly so that equilibrium exists at all times) until the string makes an angle θ with the vertical. Work done by the force F is :
Be definition of Work, Work Done = F.S. cos θ
Taking S and cos θ together like
W= F. (S cos θ)= Force × Component of displacement along force
Here Force F is acting horizontally and displacement toward right is L sin θ, So
Work done = F.L. sin θ
Question 4:
moderateAn object of mass m is tied to string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases (it is pulled extremely slowly so that equilibrium exists at all times) until the string makes an angle θ with the vertical. Work done by the gravitational force mg is :
Be definition of Work, Work Done = F.S. cos θ
Taking F and cos θ together like
W= (F. cos θ) . s = Component of Force along displacement × displacementÂ
          Here gravitational force mg is acting downwards and displacement in upward direction is (L- L cos θ), So
Work done = mg.(L-Lcosθ)cos (180°)= -mgL(1-cosθ)
Question 5:
easyA force of (3ˆi + 4ˆj)N acts on a body and displaced it by (3ˆi + 4ˆj)m . The work done by the force is
By Definition of Work ,
Work Done = F.S= (3ˆi + 4ˆj).(3ˆi + 4ˆj)= 9+16 =25 J
Question 6:
easyWhen the bob of a simple pendulum swings, the work done by tension in the string is
As Angle between tension force and displacement is 90°. Work done is zero
Question 7:
moderateA particle moves along the x-axis from x = 0 to x = 5 m under the influence of a force F (in N) given by F = 3x² –2x + 7. Calculate the work done by this force.
Work Done by Variable force is ∫F.dx, So
W= ∫(3x² –2x + 7).dx=[3x³/3-2x²/2+7x]= [x³-x²+7x]Â
Using Proper limits from x=0 to x= 5, we get
W= 125-25+35=135 J
Question 8:
moderateA force of (5 + 3x) N, acting on a body of mass 20 kg along the x-axis, displaces it from x = 2 m to x = 6 m. The work done by the force is
Work Done by Variable force is ∫F.dx, So
W= ∫(5 + 3x).dx= 5x+3x²/2
Using Limits from x=2 to x=6 we get
W= 68 J
Question 9:
moderateA person draws water from a 5m deep well in a bucket of mass 2 kg of capacity 8 litre by a rope of mass 1 kg. What is the total work done by the person ? [g = 10 m/s2]
Work Done in Pulling the Bucket + Rope System=Â
Mgh+mg(h/2)
10×10× 5 + 1×10×(5/2) =525 J
Question 10:
easyAssertion: Work done by a force depends on frame of reference.
Reason: Force and displacement both depend on frame of reference.
Work done depends on the frame of reference because displacement depends on the frame of reference. However, real forces do not depend on the frame of reference. Hence, the Assertion is true but the Reason is false.