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**Ques 1: Will the momentum remain constant if some external force acts on the system? (1)Ans:** No. it is true only for an isolated system.

if

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(a) v (the speed of the cyclist) being large.

(b) r being small

(c) The road surface being slippery.

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Lesser the value of radius of bubble ( r ), greater is the excess pressure.

(b) Cyclic process

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Thus, the pendulum will not oscillate at all, and therefore the experiment cannot be performed.

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The corresponding velocity- time graph is**Ques 10: A body of mass 5 kg is acted upon by two perpendicular forces of magnitude 8 N and 6 N. Find the magnitude and direction of the acceleration. (2)Ans: **The two perpendicular forces acting on the body are shown below in the figure.

Let =

∴

Acceleration

Direction of acceleration ( a ) will be the direction of force F , i.e.,

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When the body falls from some height, potential energy at the top equals the gain in kinetic energy. The body loses some kinetic energy and again rises to some different height.

∴ Percentage loss in K.E.

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As

Or

Thus, the rotational kinetic energy of the system increases on decreasing its moment of inertia.

OR

The change in the value of g at a height h above the Earth is same as at a depth d below it. If h and d are compared to the radius of the earth. What is the ratio (hd)? (2)

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∴

or

Substituting the values and simplifying, we get

OR

We know that, g at height h is given by

And similarly, we have g at depth d is given by

But g

∴

(ii) Distinguish between an isochoric and isobaric processes. (2)

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Here, ΔT= 0

In an adiabatic process, the total heat content ( Q ) of the system remains constant though other variables ( P and T ) may change.

In this process, ΔQ= 0

(ii) A process in which volume ( V ) remains constant though other variables ( P and T ) may change, is called an isochoric process.

In this process, ΔV= 0

An isobaric process is that for which pressure (P) of the system remains constant though other variables (V and T) may change.

In this process, ΔP= 0

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Where , V

∴

Neglecting the higher power

∴

Thus, the velocity of sound increases by 61 cm/s for every 1

W =m * 980 * 100 * 100 ergs

∴ J = 4.2 * 10

We know, heat energy

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Now,

Thus, k is not a dimensionless constant, but is a constant with dimensions.

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W is weight of the lawn roller. When pushed by applying a force at an angleθ . F cosθ moves it forward while the apparent weight becomes W +F sinθ.

However when pulled, the apparent weight becomes W -F sinθ .

Since the force of friction is directly proportional to normal reaction (equal to apparent weight of the roller), it is more when it is pushed than when is pulled.

Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the coefficient of friction between the coins and the record is 0.15. Which of the two coins will revolve with the record? (3)

Maximum force due to static force

or

∴

Solving we get,

Thus, the coin placed at 4 cm will revolve with the record.

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Integrating both sides, we get

or v

i.e.

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If the impact lasts for a small time dt and the momentum of the body changes from then,

varies with time and does not remain constant.

is a measure of the impulse of the force.

Let be the constant force during the impact, then

∴

Thus, the impulse received during an impact is equal to the total change in momentum produced during the impact.

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In case of the planet,

Dividing these two equations, we get

But g

and

∴

Thus the ratio of the mass of the planet to the mass of the Earth is 1/2 .

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(i) Which of the vessels contains more molecules?

(ii) Which of the vessels is under greater pressure and why?

(iii) In which vessel is the average molecular speed greater? How many times is it greater?(3)

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(ii) Vessel containing hydrogen will have more pressure.

Since M and V are the same in both the cases, therefore the pressure exerted by hydrogen is more than that by nitrogen.

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A diatomic molecule that can be taken as a rigid rotator with 5 degrees of freedom: 3 translational and 2 rotational. Using the law of equipartition of energy the total internal energy of a mole of such a gas is given by

Then molar specific heat at constant volume

and molar specific heat at constant pressure

(a) What values do you find in the school student?

(b) The police inspector is chasing the pickpocket on a straight road. The jeep is going at its maximum speed v. The pickpocket rides on a motorcycle when the jeep is at a distance d away and the motorcycle moves with a constant acceleration a. Show that the pickpocket will be caught if (4)

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Pickpocket will be caught if s+d = vt

t should be real.

This is possible if

OR

(a) A balloon is ascending at the rate of 14 ms-1 at a height of 98 m above the ground, when a packet is dropped from it. After how much time and with what velocity does it reach the ground?

(b) Do the following two graphs represent same types of motion? Name the motion.

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Where R is horizontal range.

(i)

(ii)

(iii)

From eq. (ii) and (iii)

or

Put (iv) in (i) , we get

Or

(a) When the packet is dropped, it has a velocity of 14ms

We have

∴

Considering only the +ve sign

v(t) = v(0) + at

Thus, the final velocity of the body is along the downward direction.

(b) Both the graphs represent non-uniform motion.

(ii) Prove that the adiabatic elasticity of the gas = γ * P , where P is pressure of the gas and being the specific heats of the gas at constant pressure and constant volume respectively. (5)

OR

The difference between the length of a certain brass rod and that of steel rod is claimed to be constant at all temperatures. Is it possible? (5)

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Bulk modulus,

When the gas is impressed isothermally, Boyle’s law holds good, i.e.

PV = constant,

Differentiating w. r. t. V , we get

or

Thus, the isothermal elasticity of a gas is equal to its pressure. When the gas is compressed adiabatically, we get

Differentiating w. r. t. V , we get

Thus, the adiabatic elasticity of a gas is γ times the pressure of the gas.

Or

At a given temperature, let the length of the brass rod be L

Let the temperature be raised to t

∴ Length of the brass rod at t

Length of the steel rod at t

∴ Here α

Difference between the lengths of the rods at t

The difference remains that same at all temperatures

Thus, the length of the rods must be inversely proportional to the linear coefficient of their materials.

OR

(i) Derive an expression for finding the velocity of an approaching aeroplane using radar waves.

(ii) An ultrasonic wave of frequency 45, 000 Hz sent out by sonar shows a frequency rise of 600 Hz on reflection from an approaching submarine. If the velocity of sound in water is 1500 ms-1. Calculate the speed of the submarine. (5)

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But F = mg

∴

Or

Where ρ is mean density of the Earth.

When the body is dropped into the straight hole and it falls through the depth d , the value of acceleration due to gravity at the point P is given by,

Where M ' is the mass of the sphere of radius ( R -d)

Thus,

or

i.e., acceleration (in magnitude) of the body is proportional to the displacement from the centre of the earth O. Thus, the motion is SHM.

Time period,

Or

(i) The radar waves sent form the Earth strike the approaching aeroplane. Here the radar is a source which is stationary and the aeroplane is an observer which is moving towards the stationary source. We have to determine the velocity to the approaching plane.

∴ Apparent frequency, =

Where n is the velocity of the radar waves and v_{s} is the velocity of the aeroplane.

Now the aero plane receives waves of frequency n ' and acts as a source moving towards stationary observer, i.e. radar on the Earth. Since on reflection, the frequency does not change, the aero plane will reflect waves of frequency n'.

∴ Apparent frequency received by the radar is given by,

Using the binomial theorem as

or

Thus, velocity of an approaching aero plane is

(ii) Substituting the values given in the above expression, we have

Thus, the speed of the submarine is 10 m/s .

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