SET 7
1. Fill in the blanksa) 1AU=1.5x108 km C = 3x108m/s C = …………… AU/s
b) Force of friction = 1.96N Normal Reaction = 19.6 μ = ……………
c) Time Period = 4 Sec Mass = 1 kg Spring Constant K = …………
d) No. of significant figures
in Area = ………………. Breadth = 2.01 cm Length = 1.00 cm
(4)
2. Mechanical power is represented by P=Fv + Av3ρ where F is the force, v is the velocity, A is the area
and ρ is the density
a) The dimensional formula of power is ………………. (1/2)
b) Check the dimensional validity of the above equation (1)
c) Which of the following equations can’t be obtained by the dimensional method?
i) =
ii) E = k mv2 iii) P= h ρg iv) N= N0e-λg (1/2)
3. Two cars A and B travelling with speed 20 m/s and 10 m/s respectively applies breaks, so that A
comes to rest in 10 seconds, B comes to rest in 15 seconds
a) Draw the velocity time graph of A and B in the same graph (1)
b) From the graph determine which of the two cars travelled further after breaks were applied and by
how much distance (2)
c) In the above process the wear and tear of which of the car get affected more (1)
4. An object is projected with velocity v at an angle θ to the horizontal
a) Obtain a mathematical expression for the range in the horizontal plane (2)
b) What are the conditions to obtain more horizontal range (1)
c) Find the maximum height of the object when its path makes an angle of 300 with the horizontal
(velocity of projection = 8 m/s) (2)
5. ⃗ and ⃗ are two non-zero vectors
a) If ⃗ ⃗ = ⃗ . ⃗, what is the angle between ⃗ and ⃗ (1)
b) Find the value of ⃗ . (⃗ x ⃗) (1)
c) The parallelogram law is used to find the resultant of two vectors. Find the magnitude of the
resultant of these two vectors in terms of their magnitude and angle between them. (3)
6.
a) A Cricket player throws his hands backward while catching a ball. Give the reason? (1)
b) When the bullet fired from a gun, the gun recoils freely. Which one has greater kinetic energy -
gun or bullet? Explain (2)
7. An electron of mass m moves with a uniform speed v around the nucleus along a circular path of
radius r.
a) Derive an expression for the acceleration of electron (2)
b) Explain why the speed of electron does not increase even though it is accelerated by the above
acceleration? (1)
8. Work is required to be done to lift a body from ground. Let the body be dropped from the height h
a) State the work - energy theorem (1)
b) Draw graphically, the variation of Kinetic Energy (K.E) and Potential Energy(P. E) with the
height of the body where do you find
i) The maximum P. E? ii) The maximum K. E? (2)
c) State and prove the law of conservation of energy in this case (3)
9. Moment of inertia of a thin ring of radius R about an axis passing through any diameter is
a) To get the moment of inertia of the same ring about an axis passing through any tangent which of
the following theorem you can use? State the theorem
i) Perpendicular axis theorem ii) Parallel axis theorem (1
)
b) What is the radius of gyration of the ring about an axis passing through any diameter? (1/2)
c) A thin metal ring of radius 0.25 m and mass 2 kg starts from rest and rolled down in an inclined
plane. If the linear velocity on reaching the foot of the plane is 2 m/s, calculate its rotational K.E.
(2)
10. When we throw a stone into the air it comes back to the earth. But if we increase the speed of the
stone, it may escape from the gravitational attraction of earth.
a) Explain the term escape velocity. (1)
b) The radius of the earth is reduced by 4% of its initial value. The mass of the earth remains
unchanged. What will be the percentage of change in the escape velocity. (2)
c) Assuming that planets move in circular orbits, derive Kepler’s third law on planetary motion. (2)
11. When longitudinal tension is given to a steel wire, it elongates
a) Name the law that gives the relation between applied force and elongation of steel wire. (1)
b) State the law (1)
c) Find out the load to be suspended at the end of a brass wire at length 18m to stretch it through
1mm. The diameter of the wire is 0.2m. Young’s Modulus = 20 GPa. (2)
12. When a fluid moving through a pipe of varying cross-sectional area, the sum of pressure energy, KE
per unit volume, PE per unit volume remains a constant.
a) Name the theorem underlying the statement. (1)
b) Derive an expression for the above theorem. (3)
13. A thermodynamic process is one in which the thermodynamic variable (P,V,T etc.) change
a) Name the thermodynamic process in which = constant (1)
b) State and explain first law of thermodynamics (2)
c) Derive an expression for the work done in an adiabatic process involving an ideal gas in terms of
pressure and volume. (2)
OR
a) Which thermodynamic process is also called an iso-entropic process (1/2)
b) The efficiency of Carnot engine is
. If on reducing the temperature of the sink by 650C its
efficiency becomes
, find the temperature of sink and source (1
)
c) Obtain the expression for the work done during an adiabatic process (3)
14. Vertical oscillation of loaded spring in water dies out rapidly
a) Name the type of oscillation here (1)
b) How can you maintain the oscillation of loaded spring in water? (1)
c) A girl swings in sitting position on a swing. How will the period of swing be affected,
if she stands up? (2)
15. A girl tries to find out the frequency of a turning fork using sonometer apparatus
a) What is the nature of wave produced in a sonometer (1)
b) Explain why the paper rider throws away at a particular resonating length? (2)
16. A train is approaching a station blowing its siren. A man standing on the plat form observes change
in frequency of the sound produced by the train
a) What is the phenomenon called (1)
b) Write down an expression for the apparent frequency heard by a stationary observer when the
source is approaching him with a velocity u? (1)
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