PHYSICS-25-02- 11th (PQRS & J) Space

FINAL TEST Class : XI Time : 90 min. Max. Marks : 90 General Remarks: INSTRUCTIONS 1. The question paper contains 15 questions and 28 pages. All questions are compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator. 2. Write your BC roll no. on top right corner of page #3 of answer sheet also. 3. Each solution should be done only in the space provided for it, otherwise the solution will not be checked. 4. Use of Calculator, Log table and Mobile is not permitted. 5. Legibility and clarity in answering the question will be appreciated. 6. Put a cross ( × ) on the rough work done by you. 7. Page 26 is an Extra page. You may use that for any unfinished question(s) mentioning the page number with remark "continued on page " 8. You can tear off the LAST PAGE carefully along the scissor marked line and take it as Final Test. Name Father's Name Class : Batch : B.C. Roll No. Invigilator's Full Name For Office Use ……………………………. Total Marks Obtained………………… Q.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Marks Take g = 10 m/s2 wherever required PART -A [6 × 5 = 30] Q.1 Two blocks A and B are joined by means of a slacked string passing over a massless pulley as shown in diagram. The system is released from rest and it becomes taut when B falls a distance 0.5 m, then (a) Find the common velocity of two blocks just after string become taut. (b) Find the magnitude of impulse on the pulley by the clamp during the small interval while string becomes taut. [2 + 3] BC Roll. No. Q.2 What is the temperature of the steel-copper junction in the steady state of the system shown in the figure. Length of the steel rod = 25 cm, length of the copper rod = 50 cm, temperature of the furnace = 300 °C, temperature of the other end = 0°C. The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel = 50 J s–1 m–1 K–1 and of copper = 400 J s–1 m–1 K–1) [5] Q.3 A source of frequency 700 Hz is placed between a man and a wall at the same height of person's ear. Find the velocity v (assume v << c) of the source with which it should approach the wall such that person will detect 3 beats per second. [Take velocity of sound = 350 m/s] [5] Q.4 A ring of radius r made of wire of density  is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Find the percentage change in tension for two percent change in angular velocity of rotation. Ignore gravity. [5] Q.5 One end of a long string of linear mass density 10–2 kg m–1 is connected to an electrically driven tuning fork of frequency 150 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves from this end have negligible amplitude. At t = 0, the left end (fork end) of the string is at x = 0 has a transverse displacement of 2.5 cm and is moving along positive y-direction. The amplitude of the wave is 5 cm. Write down the transverse displacement y (in cm) as function of x (in m) and t (in sec) that describes the wave on the string. [5] Q.6 A narrow capillary tube is dipped 10 cm below water surface and a liquid bubble of radius 2 mm formed at the lower end by blowing air through the tube. (a) Calculate the excess pressure due to surface tension. (b) What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at temperature of the experiment is 7.30 × 10–2 N m–1. 1 atmospheric pressure = 105 Pa, density of water = 1000 kg m–3. [2 + 3] PART -B [5 × 6 = 30] Q.7 A conical pendulum is composed of a mass 100 gm and a massless string of length 50 cm. It swings with constant angular velocity 5 rad/s as shown in the figure. (a) What is the angle, , between the string and the vertical? (b) What is the angular momentum vector with respect to the pivot at the instant shown in the diagram? (c) What is the torque vector with respect to the pivot at the instant shown in the diagram? [2 + 2 + 2] Q.8 A river has a width d. Afisherman in a boat crosses the river twice. During the first crossing, his goal is to minimize the crossing time. During the second crossing, his goal is to minimize the distance that the boat is carried downstream. In the first case, the crossing time is T0. In the second case, the crossing time is 3T0. What is the speed of the river flow? Find all possible answers. [6] Q.9 A frog sits on the end of a long board of length L. The board rests on a frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is the minimum take-off speed i.e. relative to ground 'v' that allows the frog to do the trick? The board and the frog have equal masses. [6] Q.10 Aheat engine uses an ideal gas ( = 1.40) that undergoes the reversible cycle shown in figure. Obtain the thermodynamic percentage efficiency of the engine. [6] Q.11 A car is moving away from a stationary target at a constant velocity of 10 m/s. Aman sitting on the top of the car fires a machine gun that can fire bullets at a constant rate of 3 bullets per second. Assuming that all the bullets hit the target and the speed of the bullets with respect to ground is 80 m/s. (neglate the gravity) (a) Find the number of bullets that hit the target in one minute. (b) Find the average thrust force experienced by the man carrying gun due to recoil if mass of each bullet is 100 gm. [3.5+2.5] PART -C [4 × 7.5 = 30] Q.12 A block of mass 160 gm is attached to a rigid support by a spring of force constant 104 N/m and it is executing simple harmonic motion with amplitude 10 cm on a horizontal, frictionless table. Abullet of mass 90 gm and speed 100 m/s strikes the block when the block passes the equilibrium (x = 0) point, going in the same direction as the bullet, as shown. The bullet remains embedded in the block. (a) Determine the amplitude and angular frequency of the resulting simple harmonic motion. (b) Write x coordinate (in cm )of combined mass as function of time, considering time of collision as t = 0. [5+2.5] Q.13 The mass distribution inside the sphere of radius 60 cm is nonuniform, so that the center of mass lies at a distance 30 cm from the geometric center. Suppose that the sphere is attached rigidly to a massless horizontal rod of length 10 cm and negligible volume, oriented along the line formed by the center of mass and the geometric center of the sphere, as shown. The rod is attached on the side of the sphere nearest to the center of mass, and the far end of the rod is attached to a fixed pivot. The entire system is submerged in water and the sphere is held stationary by a vertical string tied to its lowest point. Consider the average density of the sphere = 700 kg/m3 and density of water = 1000 kg/m3. (a) Find the force exerted by water on the sphere. (b) Find the tension T in the string. [2.5 + 5] Q.14 A weightless inextensible string which first runs over a fixed weightless pulley D and then coils on a spool B of outer radius R, and inner radius R/2 tightly. The smaller pulleywithout sliding along a horizontal fixed rail, as shown. The total mass of the spool is M. The axis O of the spool is perpendicular to the plane of the drawing and moment of inertia relative to O is 1 MR 2 . If the end Aof the string is pulled downward 2 with constant acceleration g/2, then find (a) Direction in which centre moves. (b) Acceleration of O. (c) Tension in the string. (d) Direction and magnitude of friction force between shaft and rail. [1 + 2.5 + 2 + 2] Q.15 A student has a large quantity of a flexible cable. If she cuts a piece of that cable and hangs it vertically, the longest piece that does not break under its own weight is l. The student then cuts another piece of length L and places it on a horizontal smooth table. Asmall part of that cable hangs over the edge so that the cable begins to slide down after being released. What can be the maximum value of L for which the piece does not break during the slide? [7.5] EXTRA PAGE PH YSI CS FINAL TEST Take g = 10 m/s2 wherever required PART -A [6 × 5 = 30] Q.1 Two blocks A and B are joined by means of a slacked string passing over a massless pulley as shown in diagram. The system is released from rest and it becomes taut when B falls a distance 0.5 m, then (a) Find the common velocity of two blocks just after string become taut. (b) Find the magnitude of impulse on the pulley by the clamp during the small interval while string becomes taut. [2 + 3] Q.2 What is the temperature of the steel-copper junction in the steady state of the system shown in the figure. Length of the steel rod = 25 cm, length of the copper rod = 50 cm, temperature of the furnace = 300 °C, temperature of the other end = 0°C. The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel = 50 J s–1 m–1 K–1 and of copper = 400 J s–1 m–1 K–1) [5] Q.3 A source of frequency 700 Hz is placed between a man and a wall at the same height of person's ear. Find the velocity v (assume v << c) of the source with which it should approach the wall such that person will detect 3 beats per second. [Take velocity of sound = 350 m/s] [5] Q.4 A ring of radius r made of wire of density  is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Find the percentage change in tension for two percent change in angular velocity of rotation. Ignore gravity. [5] Q.5 One end of a long string of linear mass density 10–2 kg m–1 is connected to an electrically driven tuning fork of frequency 150 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves from this end have negligible amplitude. At t = 0, the left end (fork end) of the string is at x = 0 has a transverse displacement of 2.5 cm and is moving along positive y-direction. The amplitude of the wave is 5 cm. Write down the transverse displacement y (in cm) as function of x (in m) and t (in sec) that describes the wave on the string. [5] Q.6 A narrow capillary tube is dipped 10 cm below water surface and a liquid bubble of radius 2 mm formed at the lower end by blowing air through the tube. (a) Calculate the excess pressure due to surface tension. (b) What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at temperature of the experiment is 7.30 × 10–2 N m–1. 1 atmospheric pressure = 105 Pa, density of water = 1000 kg m–3. [2 + 3] PART -B [5 × 6 = 30] Q.7 A conical pendulum is composed of a mass 100 gm and a massless string of length 50 cm. It swings with constant angular velocity 5 rad/s as shown in the figure. (a) What is the angle, , between the string and the vertical? (b) What is the angular momentum vector with respect to the pivot at the instant shown in the diagram? (c) What is the torque vector with respect to the pivot at the instant shown in the diagram? [2 + 2 + 2] Q.8 A river has a width d. A fisherman in a boat crosses the river twice. During the first crossing, his goal is to minimize the crossing time. During the second crossing, his goal is to minimize the distance that the boat is carried downstream. In the first case, the crossing time is T0. In the second case, the crossing time is 3T0. What is the speed of the river flow? Find all possible answers. [6] Q.9 A frog sits on the end of a long board of length L. The board rests on a frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is the minimum take-off speed i.e. relative to ground 'v' that allows the frog to do the trick? The board and the frog have equal masses. [6] Q.10 A heat engine uses an ideal gas ( = 1.40) that undergoes the reversible cycle shown in figure. Obtain the thermodynamic percentage efficiency of the engine. [6] Q.11 A car is moving away from a stationary target at a constant velocity of 10 m/s. A man sitting on the top of the car fires a machine gun that can fire bullets at a constant rate of 3 bullets per second. Assuming that all the bullets hit the target and the speed of the bullets with respect to ground is 80 m/s. (neglate the gravity) (a) Find the number of bullets that hit the target in one minute. (b) Find the average thrust force experienced by the man carrying gun due to recoil if mass of each bullet is 100 gm. [3.5+2.5] PART -C [4 × 7.5 = 30] Q.12 A block of mass 160 gm is attached to a rigid support by a spring of force constant 104 N/m and it is executing simple harmonic motion with amplitude 10 cm on a horizontal, frictionless table. A bullet of mass 90 gm and speed 100 m/s strikes the block when the block passes the equilibrium (x = 0) point, going in the same direction as the bullet, as shown. The bullet remains embedded in the block. (a) Determine the amplitude and angular frequency of the resulting simple harmonic motion. (b) Write x coordinate (in cm )of combined mass as function of time, considering time of collision as t = 0. [5 + 2.5] Q.13 The mass distribution inside the sphere of radius 60 cm is nonuniform, so that the center of mass lies at a distance 30 cm from the geometric center. Suppose that the sphere is attached rigidly to a massless horizontal rod of length 10 cm and negligible volume, oriented along the line formed by the center of mass and the geometric center of the sphere, as shown. The rod is attached on the side of the sphere nearest to the center of mass, and the far end of the rod is attached to a fixed pivot. The entire system is submerged in water and the sphere is held stationary by a vertical string tied to its lowest point. Consider the average density of the sphere = 700 kg/m3 and density of water = 1000 kg/m3. (a) Find the force exerted by water on the sphere. (b) Find the tension T in the string. [2.5 + 5] Q.14 A weightless inextensible string which first runs over a fixed weightless pulley D and then coils on a spool B of outer radius R, and inner radius R/2 tightly. The smaller pulley without sliding along a horizontal fixed rail, as shown. The total mass of the spool is M. The axis O of the spool is perpendicular to the plane of the drawing and moment of inertia relative to O is 1 MR 2 . If 2 the end A of the string is pulled downward with constant acceleration g/2, then find (a) Direction in which centre moves. (b) Acceleration of O. (c) Tension in the string. (d) Direction and magnitude of friction force between shaft and rail. [1 + 2.5 + 2 + 2] Q.15 A student has a large quantity of a flexible cable. If she cuts a piece of that cable and hangs it vertically, the longest piece that does not break under its own weight is l. The student then cuts another piece of length L and places it on a horizontal smooth table. A small part of that cable hangs over the edge so that the cable begins to slide down after being released. What can be the maximum value of L for which the piece does not break during the slide? [7.5]