Test Series-9

### Instructions

A. Question paper format:
• The question paper consists of Physics Part. There are 5 sections.
• Section I contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.
• Section II contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which one or more is/are correct.
• Section III contains 2 questions. Each question has four statements (A, B, C and D) given in column I and four statements (p, q, r and s ) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, match B with q and r
• Section IV contains 2 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.
• Section V contains 6 questions. The answer to each of the questions is a single - digit integer, ranging from 0 to 9.

B. Marking scheme:
• For each question in Section I you will be awarded 2 marks for the correct answer and zero mark if question is not attempted.
• For each question in Section II, you will be awarded 3 marks for the correct choice(s) for the answer, and zero mark if question is not attempted.
• For each question in Section III, you will be awarded 5 marks for correct matching of each row in column 1 to the correct answer in column 2.
• For each question in Section IV, you will be awarded 4 marks for the correct answer and zero mark if question is not attempted.
• For each question in Section V you will be awarded 2 marks for the correct answer and zero mark if question is not attempted.

SECTION-I

Single Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONLY ONE is correct
1.A heated object emits radiation which has maximum intensity at frequency m.Now if the temperature of the body is doubled,then the maximum intensity of radiation happens at the freqency
• 4m
• 2m
• m
• .5m

2.An electron of mass me initialy at rest moves through a certain distance in a uniform electric field in time t1.A proton of mass mp also initialy at rest ,takes time t2 to move through an equal distance in this uniform electric field.Neglect any effect of gravity. Which of the following equation is correct in this case
• met22 -mpt12 =0
• met12 -mpt22 =0
• met2 -mpt1 =0
• None of the above

3. In the visible region,the dispersive powers for crown and flint glass prism are ω1 and ω2 , and the mean angular deviation are d1 and d2 respectivley. When the two prism are combined ,the condition of zero dispersion by the combination is
• ${\left({\omega }_{1}{d}_{1}\right)}^{2}+{\left({\omega }_{2}{d}_{2}\right)}^{2}=0$
• ${\omega }_{1}{d}_{2}+{\omega }_{2}{d}_{1}=0$
• ${\omega }_{1}{d}_{1}+{\omega }_{2}{d}_{2}=0$
• $\sqrt{{\omega }_{1}{d}_{1}}+\sqrt{{\omega }_{2}{d}_{2}}=0$

4. A train sounds its whistle as it approaches and leaves a railroad crossing. An observer at the crossing measures a frequency of 219 hz as the train approaches and a frequncy of 184hz as th train leaves.The speed of the sound is 340m/s. Find the speed of the train and frequency of its whistle
• 26.5m/s,200hz
• 29.5m/s,150hz
• 29.5m/s,200hz
• 29.5m/s,250hz

5. A larger wooden wheel of radius R and moment of inertia I is mounted on an axle so as to rotate freely. A bullet of mass m and speed v is shot tangential to the wheel and strikes its edge ,lodging in the rim. If the wheel were originally at rest. What will be angular velocity after the collision
• $\frac{\mathrm{mvr}}{m{R}^{2}+I}$
• $\frac{m{R}^{2}}{m{\mathrm{vr}}^{}+I}$
• $\frac{m{R}^{2}}{m{\mathrm{vr}}^{}+\mathrm{2I}}$
• None of the above

SECTION-II

Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONE OR MORE is/are correct.
6.Centrifugal force is an inertial force when considered by
• An observer who is moving with the particle that experience the force
• an outside observer
• An observer at the center of the circular motion
• None of the above

7. Choose the correct statement
• Two important differences between viscous forces and frictional forces are that viscous force depends upon the temperature and also velocity profile for the liquid where as frictional forces is usually independent of such items
• The terminal velocity of a spherical body falling in a fluid depends on the diamter and density of the body as well the density and viscosity of the fluid
• M drops of a fluid ,each with surface energy k,join to form a single drop,the amount of energy released in the process is K(m-m2/3
• Tiny insects can float and walk on the surfac of water due to both buoyancy and surface tension

8.A nearly massless rod is pivoted at one end so it can freely swing as a pendulum.Two masses 2m and m are attached to it at distance a and 3a respectively from the pivot end. The rod is held horizontal and then released. Which of the following is correct?
• The angular acceleration at the instant it is released 5g/11a
• Moment of inertia of the system about pivot is 11ma2
• The angular acceleration at the instant when the rod makes an angle ? with horizontal 5gcosθ/11a
• The net torque about the pivot end becomes zero when rod becomes vertical.

9.A particle is constraint to move along x-axis acted by a force whose potential energy is given by
U=2x3-15x2+36x+100
Choose the correct option
• The force acting on the particle is 6x2-30x+36
• If it is slightly displaced from x=3,it will oscillate
• The minimum KE required at origin to reach at x=1 will be 23J
• The minimum KE required at origin to reach at x=2 will be 28J

10.Blocks A and B of mass 3 Kg and 2 Kg respectively ,placed on the horizontal smooth surface.They are connected by a massless spring. Block A is given a kicks which imparts a velocity of 10m/s to its towards B
• The velocity of the Center of mass of the system remains constant through out the motion and its value is 6m/s
• The velocity of block B in Center of mass frame at t=0 is -6m/s
• The velocity of block A in Center of mass frame at t=0 is 4m/s
• Total energy of the system is 150J

SECTION-III

Matrix - Match Type
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II.

11.
 Column-I Column-II A) A particle moving with constant velocity on a horizontal plane p) P=constant B) Motions of object under central forces q) L=constant C) A object fired from a gun explodes in air r) K.E=constant D) A object in Uniform circular motion in horizontal plane s) PE is constant

• A(p,r,s),B(q),C(p,q),D(q,r,s)
• A(p,q,r,s),B(q,r),C(p),D(q,r,s)
• A(p,q,r,s),B(p),C(p),D(q,r,s)
• A(p,q,r,s),B(q),C(p),D(q,r,s)

12.
 Column-I Column -II A) A 5g bullet going 300m/s strikes a 1.995 kg wooden block which is bob of a balistic pendulum,the height which the center of gravity of bullet-block system reaches above the initial position of the center of gravity p) 34.5 m B) A ball is thrown upward with initial velocity 15m/ at an angle 300 with the horizontal The thrower stand near the top of a long hill which slopes downward at an angle 200.How far down the slope the ball strikes( given tan20=.364) q) .017m C) How high does methyl alcohol rise in a glass tube .07 cm in diameter.Surface tension=.023 N/m and density of alcohol=.8 g/cm3 r) 90m D) A 1200kg truck going with 30m/s applies its brakes and skids to rest.If the friction force between sliding tires and pavement is 6000N,how far does the car skid before coming to rest s) .0287m
• A(s),B(p),C(r),D(q)
• A(p),B(s),C(q),D(r)
• A(s),B(q),C(p),D(r)
• A(s),B(p),C(q),D(r)

SECTION-IV

A pendulum is constructed from two identical uniform rods a and b each of lenght L and mass M,connected at right angles to form a T by joining the center of rod a to one end of the rod b. The T pendulum is then suspended from free end of rod b and pendulum swings in the plane of T

13.The moment of inertia of T about the axis of rotation
• 11ML2/12
• 7ML2/12
• 17ML2/18
• 17ML2/12

14.The potential energy change of the T when it is rotated by angle η from vertical position
• $\frac{3\mathrm{Mg}}{L}\left(1-\mathrm{cos}\theta \right)$
• $\frac{3\mathrm{Mg}}{L}\left(1-\mathrm{sin}\theta \right)$
• $\frac{4\mathrm{Mg}}{L}\left(1-\mathrm{sin}\theta \right)$
• $\frac{2\mathrm{Mg}}{L}\left(1-\mathrm{sin}\theta \right)$

15.For small angle with vertical position,The T makes SHM,the angular frequency
• $\sqrt{\frac{2g}{17L}}$
• $\sqrt{\frac{17g}{19L}}$
• $\sqrt{\frac{12g}{11L}}$
• $\sqrt{\frac{18g}{17L}}$

SECTION-V

This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 10.
16.Two blocks of mass m1=m2=3Kg are connected by a light string.They are placed on a rough horizontal surface. A force of magnitude 20N is applied in the horizontal direction on a block,So that both the masses move with acceleration .5m/s2.Let T be the tension in the string.The value of T/10 is
• 1
• 2
• 4
• 3

17.A body executing linear SHM has a velocity of 3 cm/s when its displacement is 4 cm and velocity of 4 cm/s when its displacement is 3 cm. Find the amplitude of oscillation
• 2 cm
• 3 cm
• 4 cm
• 5 cm

18.If earth were to suddenly contract to half of its present size with out change in any mass.What will be the duration of the day?
• 4
• 8
• 10
• 6

19.Ionization potential of hydrogen atom is 13.6V.Hydrogen in the ground state is excited by monochromotic radaition of photons of energy 12.1 eV.The number of spectral lines emitted by the hydrogen atom according to Bohr's thoery will be
• 1
• 2
• 3
• 4

20.A spherical surface of radius of curvature R seperates air(refractive index 1.0) from glass (refractive index 1.5).The center of curvature is in the glass .A point object S1 placed in air is found to have a real image S2 in the glass.The line S1S2 cuts the surface at point O such that S1O=OS2. The value of S1O/R is
• 4
• 1
• 3
• 5