हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

(A) → R = 1 M ∑ I M I → R I and (B) → a C M = → F M in a Noninertial Frame - Physics

Advertisements
Advertisements

प्रश्न

Consider the following the equations
(A) \[\vec{R} = \frac{1}{M} \sum_i m_i \vec{r_i}\] and
(B) \[\vec{a}_{CM} = \frac{\vec{F}}{M}\] 
In a noninertial frame

विकल्प

  • both are correct

  • both are wrong

  •  A is correct but B is wrong

  •  B is correct but A is wrong.

MCQ

उत्तर

 A is correct but B is wrong

In a non-inertial frame, the position of centre of mass of the particle does not change but an additional pseudo force acts on it.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Centre of Mass, Linear Momentum, Collision - MCQ [पृष्ठ १५७]

APPEARS IN

एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
अध्याय 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 1 | पृष्ठ १५७

संबंधित प्रश्न

You are waiting for a train on a railway platform. Your three-year-old niece is standing on your iron trunk containing the luggage. Why does the trunk not recoil as she jumps off on the platform?


You are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of the cage? Does it makes a difference whether the cage is completely closed or it has rods to let air pass?


A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass


Three particles of masses 1.0 kg, 2.0 kg and 3.0 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Locate the centre of mass of the system.  


The balloon, the light rope and the monkey shown in figure are at rest in the air. If the monkey reaches the top of the rope, by what distance does the balloon descend? Mass of the balloon = M, mass of the monkey = m and the length of the rope ascended by the monkey = L. 


During a heavy rain, hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s. Suppose 2000 hailstones strike every square meter of a 10 m × 10 m roof perpendicularly in one second and assume that the hailstones do not rebound. Calculate the average force exerted by the falling hailstones on the roof. Density of a hailstone is 900 kg/m3.


Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track(In the following figure). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off. 


Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process. 


Two balls having masses m and 2m are fastened to two light strings of same length l (See figure). The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocity of the balls just after their collision. (b) How high will the ball rise after the collision?


Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of length L (see the following figure). The system translates on a frictionless horizontal surface with a velocity \[\nu_0\] in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find
(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the centre of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.

[Hint : The light rod will exert a force on the ball B
only along its length.]


The centre of mass of a system of particles does not depend upon, ______


Find out the centre of mass for the given geometrical structures.

a) Equilateral triangle

b) Cylinder

c) Square


Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:

  1. Show pi = p’+ miV Where pi is the momentum of the ith particle (of mass mi)  and p′ i = mi v′ i. Note v′ i is the velocity of the ith particle relative to the centre of mass. Also, prove using the definition of the centre of mass `sum"p""'"_"t" = 0`
  2. Show K = K′ + 1/2MV2

    where K is the total kinetic energy of the system of particles, K′ is the total kinetic energy of the
    system when the particle velocities are taken with respect to the centre of mass and MV2/2 is the
    kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the
    system). The result has been used in Sec. 7.14.

  3. Show where `"L""'" = sum"r""'"_"t" xx "p""'"_"t"` is the angular momentum of the system about the centre of mass with
    velocities taken relative to the centre of mass. Remember `"r"_"t" = "r"_"t" - "R"`; rest of the notation is the standard notation used in the chapter. Note L′ and MR × V can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
  4. Show `"dL"^"'"/"dt" = ∑"r"_"i"^"'" xx "dP"^"'"/"dt"`
    Further show that `"dL"^'/"dt" = τ_"ext"^"'"`
    Where `"τ"_"ext"^"'"` is the sum of all external torques acting on the system about the centre of mass.
    (Hint: Use the definition of centre of mass and third law of motion. Assume the internal forces between any two particles act along the line joining the particles.)

Which of the following points is the likely position of the centre of mass of the system shown in figure?


The density of a non-uniform rod of length 1 m is given by ρ(x) = a(1 + bx2) where a and b are constants and 0 ≤ x ≤ 1. The centre of mass of the rod will be at ______.


(n – 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.


A uniform square plate S (side c) and a uniform rectangular plate R (sides b, a) have identical areas and masses (Figure).


Show that

  1. IxR/IxS < 1
  2. IyR/IyS > 1
  3. IzR/IzS > 1

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×