# Equations of Motion

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• Q1

a. (1) State Newton’s second law of motion. Calculate the force required to impart a velocity of 20 m/s in 5 s to a car at rest. The mass of the car is 1500 kg.

(2)For how long a force of 200 N acts on a body of mass 40 kg so that it can acquire a velocity of 200 m/s? [4]

b. A freely falling ball eventually stops on reaching the ground. What happens to its kinetic energy? Give suitable explanation for it. [3]

c. What do you understand by the term weight? State the units of weight in C.G.S. and S.I. system. Name the device used for measuring weight.

What will be the weight of a person of mass 20 kg on the moon? [3]

Marks:10

a. (1) Newton’s Second Law of Motion: It states that the rate of change of linear momentum of a body is directly proportional to the force applied on it and the change takes place in the direction of force.

Here,

Final velocity, v = 20 m/s; Initial Velocity, u = 0

Time taken, t = 5 s; Mass of car, m = 1500 kg

(2)

b.

When a freely falling ball eventually stops on the ground, its kinetic energy appears in the form of:

(i)heat energy i.e., the ball and the ground become warmer due to collision.

(ii)sound energy is produced due to collision of the ball with the ground.

(iii)Potential energy of configuration of the body and the ground may be changed i.e., the ball may be deformed and the ground may be depressed at the place of collision.

The process in which the kinetic energy of a freely falling ball is lost in an unproductive chain of energy is called dissipation of energy.

c.

Weight: It is a force with which a body is attracted towards the earth.

Units of weight:

In C.G.S. system: dyne

In S.I. system: newton

Spring balance is a device used for measuring weight.

Person’s mass = 20 kg

Weight of the person on the earth, W = mg

W = 20kg x 9.8m/s2 = 196N

Weight of the person on the moon, Wm = (1/6) x weight of the person on the earth

Wm = (1/6) x 196N = 32.67N

• Q2

a. The diagram shows the main scale and vernier scale of a calliper, which is used to measure the diameter of a metal ball (sphere). Find the radius of the ball. [3]

b. (i) Write the steps to estimate the order of magnitude of a given quantity.

(ii) Express the order of magnitude of the quantity 123456. [3]

c.

(i) An object is immersed in different types of liquids. Does the object experience same buoyant force in each case?

(ii) A cylindrical shaped object of cross-sectional area 0.0004 m2 and length 0.30 m is immersed completely in water. Determine

(a) Weight of the solid in SI system.

(b) Upthrust acting on solid in SI system.

(c) Apparent weight of solid in water [4]

[Take g = 10ms-2; density of water = 1000 kgm-3, density of solid = 1500 kgm-3]

Marks:10

a. In vernier scale there is 10 divisions which is in 1mm.

Therefore, least count = 1mm/10

= 0.1cm/10

= 0.01cm

In the above figure, the M.S. reading = 3.7 cm

Coinciding V.S. reading = 4

Now the diameter of the sphere ball can be calculated by the following formula:

Diameter=M.S. reading+ (coinciding V.S. reading x L.C.)

= 3.7cm + (4 x 0.01cm)

= 3.7cm + 0.04cm

= 3.74cm

b. (i) In order to perform order-of-magnitude estimations, we need to:

(a) Round all numbers involved to one significant figure and their powers of 10.

(b) Perform the necessary calculations.

(c) Round off the final result to one significant figure.

The order of magnitude of the quantity will be:

123456 = 100000 = 105 (On rounding off to the power of 10)

c. (i) The buoyant force acting on the object having volume V when immersed in a liquid of density d is given by F = V × d × g. As we know, that different liquids have different densities, so different magnitude of buoyant force acts on the object when it is immersed in different liquids.

• Q3

a. State the correction if (i) Positive error is 8 divisions (ii) Negative error is 8 divisions, when the least count is 0.01cm. [2]

b. A plastic ball is released under water. It comes to the surface of the water and doesn’t sinks in it. Explain the reason. [2]

c.Find out the acceleration of the graph line AC, given below. [2]

d. State two important precautions for drawing a graph line. [2]

e. A moving train is brought to rest within 20 sec by applying brakes. Find the initial velocity, if the retardation due to brakes is 2 m/s2.[2]

Marks:10

a. The correction can be calculated by the following formula:
i. For positive zero error, the correction is:
Correction = - (coinciding division of V.S.) x L.C.
Correction = - (8) x 0.01cm
= - 0.08cm
ii. For negative zero error, the correction is:
Correction = (n - coinciding division of V.S.) x L.C.
Correction = (10 - 8) x 0.01cm
= 0.02cm

b. When an object is released under water, there are two forces acting on it, i.e., the weight of the object acting downwards and the buoyant force acting in upwards direction. If the value of weight of the object is greater than the value of buoyant force, the object sinks in water. On the other hand, if the value of buoyant force is greater, the object floats on the surface of the water. In case of the plastic ball, due to less density of the plastic, the weight of the ball is less than the buoyant force acting on it. Hence, ball comes to the surface of water.

c. The slope of the graph line AC, i.e., (AB/BC) gives the acceleration.

d.Two main precautions for drawing the graph line are given below:
1. The graph line should be single, thin, sharp and straight.
2. It is not necessary that graph line should pass through maximum number of points. It can be passes closest to maximum number of points, which appear on either side of the line.

e. Final velocity, v = 0 (rest)
Since, Retardation = -ve acceleration
Therefore, a = - 2 m/s2

Using the first equation of motion,

v = u + at

Subsituting the given values,

0 = u + (-2) × 20

or, 0 = u – 40
or, u = 40 ms-1

• Q4

a. Calculate the increase in length of brass rod when it is heated to 770oC. Initially its length is 100cm at 10oC. Also, calculate the length at 770oC. [Take = 0.000018/o C] [2]

b. Why do water pipelines often burst in winters? [2]

c. If the radius of curvature of a spherical mirror is 30cm, calculate its focal length. [2]

d. Why are convex mirrors used as rear view mirrors in automobiles? [2]

e. The magnification “m” for a mirror is +1. What does this signify? [2]

Marks:10

a.

b. Water pipelines burst in winters: This is due to the anomalous expansion of water. At sub-zero temperature, water freezes and expands. As ice expands, it exerts large amount of pressure and bursts open the pipes because there is no space within the pipes for the expansion of ice.

c.

d. Convex mirrors are used as rear-view mirrors in automobiles as they always produce erect images. The size of an image formed is much smaller, so they give wider field of view.

e. Positive sign signifies that image is erect with respect to the object and magnitude “1” signifies that height of the image is equal to the height of object.

• Q5

a. Define a physical balance and a beam balance with the help of a clear diagram. [2]

b. Determine the force of gravitational attraction between the earth of mass 6 x 1024kg and a physics student having mass 60-kg, if the student is standing at sea level at a distance of 6.4 x 106 m from the earth’s centre. [2]

c. Two blocks made of different materials identical in shape and size are acted upon by equal forces which cause them to slide on a horizontal surface. The acceleration of the second block is found to be 2 times that of the first. What is the ratio of the mass of the first block to second block? [2]

d. On a hot summer day, the water in a swimming pool remains comfortably cool. Explain. [2]

e. Why do people wear light coloured clothes in summer and dark coloured clothes in winter? [2]

Marks:10

a. Physical balance: It is more accurate balance which can show even very small differences in mass.

It is used for measuring mass of costly substances such as gold, silver, diamonds etc.

Beam balance: It is a balance consisting of a lever with two equal arms and a pan suspended from each arm.

b. Mass of the earth, m1 = 6 x 1024kg,

Mass of the student, m2 = 60 kg,

G = 6.67 x 10-11 N-m2/kg2 and

Distance between earth’s centre and sea level, d = 6.4 x 106 m

c. :

d. On a hot summer day the water in a summing pool remains comfortably cool because of high specific heat capacity of water. Due to this the rise in temperature of water is very low as compared to the rise in temperature of land mass for the same amount of heat supplied.

e. People wear light coloured cotton clothes during summer because they keep us cool as they absorb less radiant heat or they reflect most of the heat falling on it.

People wear dark coloured clothes in winter because they keep us warm as they absorb most of radiation.