Balbharati solutions for Physics [English] 11 Standard Maharashtra State Board chapter 4 - Laws of Motion [Latest edition]

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Consider the following pair of forces of equal magnitude and opposite directions:

P. Gravitational forces exerted on each other by two-point masses separated by a distance.

Q. Couple of forces used to rotate a water tap.

R. Gravitational force and normal force experienced by an object kept on a table.

For which of these pair/pairs the two forces do not cancel each other’s translational effect?

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Consider following forces: (w) Force due to tension along a string, (x) Normal force given by a surface, (y) Force due to air resistance, and (z) Buoyant force or upthrust given by a fluid.
Which of these are electromagnetic forces?

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At a given instant three-point masses m, 2m and 3m are equidistant from each other. Consider only the gravitational forces between them. Select correct statement/s for this instance only:

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The rough surface of a horizontal table offers a definite maximum opposing force to initiate the motion of a block along with the table, which is proportional to the resultant normal force given by the table. Forces F₁ and F₂ act at the same angle T with the horizontal and both are just initiating the sliding motion of the block along with the table. Force F₁ is a pulling force while the force F2 is a pushing force. F₂ > F₁, because

A mass 2 m moving with some speed is directly approaching another mass m moving with double speed. After some time, they collide with a coefficient of restitution of 0.5. The ratio of their respective speeds after the collision is ______.

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A uniform rod of mass 2m is held horizontal by two sturdy, practically inextensible vertical strings tied at its ends. A boy of mass 3m hangs himself at one-third length of the rod. The ratio of the tension in the string close to the boy to that in the other string is

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Select the wrong statement about the centre of mass:

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For which of the following objects will the center of mass not be at their geometrical center?

(I) An egg
(II) a cylindrical box full of rice
(III) a cubical box containing assorted sweets

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In the following table, every entry on the left column can match with any number of entries on the right side. Pick up all those and write respectively against A, B, C and D.

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In real life, objects never travel with uniform velocity, even on a horizontal surface, unless something is done? Why is it so? What is to be done?

For the study of any kind of motion, we never use Newton’s first law of motion directly. Why should it be studied?

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Are there any situations in which we cannot apply Newton’s laws of motion? Is there any alternative for it?

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You are inside a closed capsule from where you are not able to see anything about the outside world. Suddenly you feel that you are pushed towards your right. Can you explain the possible cause (s)? Is it a feeling or a reality? Give at least one more situation like this.

Among the four fundamental forces, only one force governs your daily life almost entirely. Justify the statement by stating that force.

Find the odd man out:

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You are sitting next to your friend on ground. Is there any gravitational force of attraction between you two? If so, why are you not coming together naturally? Is any force other than the gravitational force of the earth coming in the picture?

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Distinguish between real and pseudo force.

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Distinguish between conservative and nonconservative forces.

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Distinguish between contact and non-contact forces

Distinguish between inertial and non-inertial frames of reference.

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State the formula for calculating work done by a force. Are there any conditions or limitations in using it directly? If so, state those clearly. Is there any mathematical way out for it? Explain.

Justify the statement, “Work and energy are the two sides of a coin.”

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From the terrace of a building of height H, you dropped a ball of mass m. It reached the ground with speed v. Is the relation mgh = `1/2"mv"^2` applicable exactly? If not, how can you account for the difference? Will the ball bounce to the same height from where it was dropped?

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State the law of conservation of linear momentum. It is a consequence of which law? Give an example from our daily life for the conservation of momentum. Does it hold good during the burst of a cracker?

Define coefficient of restitution.

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Obtain its value for an elastic collision and a perfectly inelastic collision.

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Discuss the following as special cases of elastic collisions and obtain their exact or approximate final velocities in terms of their initial velocities.

1. Colliding bodies are identical.
2. A very heavy object collides on a lighter object, initially at rest.
3. A very light object collides on a comparatively much massive object, initially at rest.

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A bullet of mass m₁ travelling with a velocity u strikes a stationary wooden block of mass m₂ and gets embedded into it. Determine the expression for loss in the kinetic energy of the system. Is this violating the principle of conservation of energy? If not, how can you account for this loss?

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One of the effects of a force is to change the momentum. Define the quantity related to this and explain it for a variable force. Usually, when do we define it instead of using the force?

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While rotating an object or while opening a door or a water tap we apply a force or forces. Under which conditions is this process easy for us? Why? Define the vector quantity concerned. How does it differ for a single force and for two opposite forces with different lines of action?

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Why is the moment of a couple independent of the axis of rotation even if the axis is fixed?

Explain balancing or mechanical equilibrium. The linear velocity of a rotating fan as a whole is generally zero. Is it in mechanical equilibrium? Justify your answer.

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Why do we need to know the center of mass of an object? For which objects, its position may differ from that of the center of gravity?

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A truck of mass 5 ton is travelling on a horizontal road with 36 km hr^-1, stops on traveling 1 km after its engine fails suddenly. What fraction of its weight is the frictional force exerted by the road? If we assume that the story repeats for a car of mass 1 ton i.e., car moving at the same speed stops at a similar distance, how much will the fraction be?

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A lighter object A and a heavier object B are initially at rest. Both are imparted with the same linear momentum. Which will start with greater kinetic energy: A or B or both will start with the same energy?

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As I was standing on a weighing machine inside a lift it recorded 50 kg wt. Suddenly for a few seconds, it recorded 45 kg wt. What must have happened during that time? Explain with complete numerical analysis.

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The figure below shows a block of mass 35 kg resting on a table. The table is so rough that it offers a self-adjusting resistive force 10% of the weight of the block for its sliding motion along with the table. A 20 kg wt load is attached to the block and is passed over a pulley to hang freely on the left side. On the right side, there is a 2 kg wt pan attached to the block and hung freely. Weights of 1 kg wt each, can be added to the pan. Minimum how many and maximum how many such weights can be added into the pan so that the block does not slide along the table?

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Power is the rate of doing work or the rate at which energy is supplied to the system. A constant force F is applied to a body of mass m. Power delivered by the force at time t from the start is proportional to ______.

Derive the expression for power in terms of F, m, and t.

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Derive the expression for power in terms of F, m, and t.

40000 litre of oil of density 0.9 g/cc is pumped from an oil tanker ship into a storage tank at 10 m higher level than the ship in half an hour. What should be the power of the pump?

Ten identical masses (m each) are connected one below the other with 10 strings. Holding the topmost string, the system is accelerated upwards with acceleration g/2. What is the tension in the 6th string from the top (Topmost string being the first string)?

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Two galaxies of masses 9 billion solar mass and 4 billion solar mass are 5 million light-years apart. If, the Sun has to cross the line joining them, without being attracted by either of them, through what point it should pass?

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While decreasing linearly from 5 N to 3 N, a force displaces an object from 3 m to 5 m. Calculate the work done by this force during this displacement.

Variation of a force in a certain region is given by F = 6x² – 4x – 8. It displaces an object from x = 1 m to x = 2 m in this region. Calculate the amount of work done.

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A ball of mass 100 g dropped on the ground from 5 m bounces repeatedly. During every bounce, 64% of the potential energy is converted into kinetic energy. Calculate the following:

1. Coefficient of restitution.
2. The speed with which the ball comes up from the ground after the third bounce.
3. The impulse was given by the ball to the ground during this bounce.
4. Average force exerted by the ground if this impact lasts for 250 ms.
5. The average pressure exerted by the ball on the ground during this impact if the contact area of the ball is 0.5 cm².

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A spring ball of mass 0.5 kg is dropped from some height. On falling freely for 10 s, it explodes into two fragments of mass ratio 1:2. The lighter fragment continues to travel downwards with a speed of 60 m/s. Calculate the kinetic energy supplied during the explosion.

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A marble of mass 2m travelling at 6 cm/s is directly followed by another marble of mass m with double speed. After a collision, the heavier one travels with the average initial speed of the two. Calculate the coefficient of restitution.

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A 2 m long wooden plank of mass 20 kg is pivoted (supported from below) at 0.5 m from either end. A person of mass 40 kg starts walking from one of these pivots to the farther end. How far can the person walk before the plank topples?

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A 2 m long ladder of mass 10 kg is kept against a wall such that its base is 1.2 m away from the wall. The wall is smooth but the ground is rough. The roughness of the ground is such that it offers a maximum horizontal resistive force (for sliding motion) half that of normal reaction at the point of contact. A monkey of mass 20 kg starts climbing the ladder. How far can it climb along the ladder? How much is the horizontal reaction at the wall?

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Four uniform solid cubes of edges 10 cm, 20 cm, 30 cm and 40 cm are kept on the ground, touching each other in order. Locate centre of mass of their system.

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A uniform solid sphere of radius R has a hole of radius R/2 drilled inside it. One end of the hole is at the center of the sphere while the other is at the boundary. Locate center of mass of the remaining sphere.

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In the following table, every item on the left side can match with any number of items on the right-hand side. Select all those.