10.) If the percentage error in the measurement ofmomentum and mass of

1.	10.) If the percentage error in the measurement ofmomentum and mass of an object are 2% and 3%respectively, then maximum percentage error in thecalculated value of its kinetic energy is(1) 2%(3) 5%(2) 1%(4) 7%
Answer» Kinetic Energy(K) = 1/2× mv²where, m = mass of the body and v = velocity.Now, Obtaining the Formula in terms of the Momentum. ∵ p = mv⇒ v = p/m ∴ K = 1/2 × m (p/m)²⇒ K = p²/2m⇒ p² = K × 2m Now, Solving the Question. ∵ p² = K × 2m∴ Taking Logarithms on both the sides of the above equation.log p² = log( k 2m)⇒ 2log p = log K+ log 2m⇒ log K = 2 log p - log 2m Now, Differentiating the both sides of the Equation, ∴ dK/K = 2(dp/p) - dm/m ∴ \|dK/K\|max. = 2\|2/100\| + \|-3/100\|⇒ \|dK/K\| = 2× 0.02 + 0.03⇒ \|dK/K\|max. = 0.07 ∴ Maximum % Error in the Kinetic Energy K is 0.07× 100 % = 7%.

10.) If the percentage error in the measurement ofmomentum and mass of an object are 2% and 3%respectively, then maximum percentage error in thecalculated value of its kinetic energy is(1) 2%(3) 5%(2) 1%(4) 7%

Answer»

Kinetic Energy(K) = 1/2× mv²where, m = mass of the body and v = velocity.Now, Obtaining the Formula in terms of the Momentum.

∵ p = mv⇒ v = p/m

∴ K = 1/2 × m (p/m)²⇒ K = p²/2m⇒ p² = K × 2m

Now, Solving the Question.

∵ p² = K × 2m∴ Taking Logarithms on both the sides of the above equation.log p² = log( k 2m)⇒ 2log p = log K+ log 2m⇒ log K = 2 log p - log 2m

Now, Differentiating the both sides of the Equation,

∴ dK/K = 2(dp/p) - dm/m

∴ |dK/K|max. = 2|2/100| + |-3/100|⇒ |dK/K| = 2× 0.02 + 0.03⇒ |dK/K|max. = 0.07

∴ Maximum % Error in the Kinetic Energy K is 0.07× 100 % = 7%.

Discussion

No Comment Found

Related InterviewSolutions

7. A body has a weight 50 N in air. Afterimmersing completely in liquid its weight is20 N. Then, the buoyant force on the bodywill be
Name the particulate which causes the disease mentioned below:(a)minamata (b)silicosis.
- Where does a body weight more at the surface of the carth or in a mine?
DelyAbody79entire chainthe ch.57. A body of mass 50gm collides elastically with anotherbody of mass 30 gm at rest. Then the percentage lossof the velocity of the colliding body during collision is1) 25% 2) 75% 3) 50% 4) 67%3) 120380.beide
What will be the acceleration of a body of mass5 kg if a force of 200 N is applied on it?
Rig. 5.168.13 Two bodles of masses 10 kg and 20 kg respectively kept on a smooth, hortzontalsurface are tied to the ends of a light string a horizontal force F 600 Nsapplied to lu A (t) B along the direction of string. What is the tension in thestring in each case
culate the gravitational force befween two protons kept at a distance67 x 10-27 kg. (1 femtometre = 10-15 m)
15. A uniform chain of length 2 m is kept on atable such that a length of 60 cm hangs freelyfrom the edge of the table. The total mass ofthe chain is 4 kg. What is the work done inpulling the entire chain onto the table ?(g = 10 m/s)1) 7.2J273.63) 120J4) 1200
Two block of mass 3 kg and 6 kg respectively are placed on a smooth 1.0 m/shorizontal surface. They are connected by a light spring of force 3 kgconstant k 200 N/m. Initially the spring is unstretched. The indicatedzmvelocities are imparted to the blocks. The maximum extension of thespring will be:A30 cm(C) 20 cm2.0 mls(B) 25 cm(D) 15 cm
88. A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the accelerationof the stone be 9.8 m/s directed towards the ground, calculate the initial velocity of the stone with which itis thrown upwards.