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Two Fat Astronauts Each of Mass 120 Kg Are Travelling in a Closed Spaceship Moving at a Speed of 15 Km/S in the Outer Space Far Removed - Physics

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प्रश्न

Two fat astronauts each of mass 120 kg are travelling in a closed  spaceship moving at a speed of 15 km/s in the outer space far removed from all other material objects. The total mass of the spaceship and its contents including the astronauts is 660 kg. If the astronauts do slimming exercise and thereby reduce their masses to 90 kg each, with what velocity will the spaceship move?

योग

उत्तर

According to the question, the spaceship is removed from all other material objects and kept totally isolated from the surroundings. Thus, the mass loss by astronauts couldn't slip away from the spaceship. Therefore, the total mass of the spaceship remains unchanged and so does its velocity.

Hence, the spaceship moves with the speed of 15 km/s.

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अध्याय 9: Centre of Mass, Linear Momentum, Collision - Exercise [पृष्ठ १६१]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
अध्याय 9 Centre of Mass, Linear Momentum, Collision
Exercise | Q 23 | पृष्ठ १६१

संबंधित प्रश्न

If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?


The centre of mass is defined as \[\vec{R} = \frac{1}{M} \sum_i m_i \vec{r_i}\]. Suppose we define "centre of charge" as \[\vec{R}_c = \frac{1}{Q} \sum_i q_i \vec{r_i}\] where qi represents the ith charge placed at \[\vec{r}_i\] and Q is the total charge of the system.
(a) Can the centre of charge of a two-charge system be outside the line segment joining the charges?
(b) If all the charges of a system are in X-Y plane, is it necessary that the centre of charge be in X-Y plane?
(c) If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?


Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an Acceleration


The centre of mass of a system of particles is at the origin. It follows that


Calculate the velocity of the centre of mass of the system of particles shown in figure.


Two blocks of masses 10 kg and 30 kg are placed along a vertical line. The first block is raised through a height of 7 cm. By what distance should the second mass be moved to raise the centre of mass by 1 cm? 


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.


In an elastic collision


A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the minimum and the maximum value of u. 


A block of mass m is placed on a triangular block of mass M which in turn is placed on a horizontal surface as shown in figure. Assuming frictionless surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.


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.]


A body of mass 2 kg is acted upon by two forces each of magnitude 1 N and inclined at 60° with each other. The acceleration of the body in m/s is ____________. [cos 60° = 0.5]


The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth?


A mass of 1kg is suspended by a string. It is first lifted up with an acceleration of 4.9 m/s2 and then lowered down with same acceleration. The ratio of tensions in the string in the two cases, respectively is g = 9.8 m/s2 ______.


A shell of mass 'M' initially at rest suddenly explodes in three fragments. Two of these fragments are of mass 'M/4' each, which move with velocities 3 ms-1 and 4 ms-1 respectively in mutually perpendicular directions. The magnitude of velocity of the third fragment is ______.


In rotational motion of a rigid body, all particles move with ______.


Figure shows a lamina in x-y plane. Two axes z and z ′ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following are true? (The point P is closer to z′-axis than the z-axis.)

  1. Torque τ caused by F about z axis is along `-hatk`.
  2. Torque τ′ caused by F about z′ axis is along `-hatk`.
  3. Torque τ caused by F about z axis is greater in magnitude than that about z axis.
  4. Total torque is given be τ = τ + τ′.

Find the centre of mass of a uniform (a) half-disc, (b) quarter-disc.


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