PHYSICS-19-11- 11th (PQRS) space

REVIEW TEST-6 Class : Time : 100 min Max. Marks : 100 INSTRUCTIONS General Remarks: 1. The question paper contain 20 questions and 29 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. Each question should be done only in the space provided for it, otherwise the solution will not be checked. 3. Use of Calculator, Log table and Mobile is not permitted. 4. Legibility and clarity in answering the question will be appreciated. 5. Put a cross ( × ) on the rough work done by you. 6. All questions carry 5 marks each. Name Father's Name Class : XI Batch : P B.C. Roll No. Invigilator's Full Name Useful Data: (i) sin 370 = 3/5; cos 370 = 4/5 ; tan370 = 3/4 (ii) sin 530 = 4/5 ; cos 530 = 3/5 ; tan530 = 4/3 (iii) g = 10m/s2 Expected Marks Important Instruction: Tampering with the answer sheet or changing the answers, after the answer sheet is evaluated will be strictly penalized. 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 Q.1 An electric scooter has a battery capable of supplying 120 Watt-hour of energy. If friction and other losses are 40% of the energy, what height can a rider achieve when driving in hilly area, if the rider and scooter have a combined weight of 900 N? Ans: h = Q.2 Two trains start simultaneously from two towns Aand B located at a distance d from each other on the same track in opposite directions. Both trains move with constant speed v towards each other. Abee is initially sitting on the front of the train starting from town A. As the train pulls out of town A, the scared bee takes off and flies with velocity u > v along the track towards B. As soon as it encounters the other train, it turns back towards A and again scared on reaching first train. It continues flying between the trains with speed u until the end. Find the total distance (s) travelled by the bee before it is crushed by the two trains. Ans: s = Q.3 A spaceship is moving with constant speed v0 in gravity free space along +Y-axis suddenly shoots out one third of its part with speed 2v0 along + X-axis. Find the speed of the remaining part. Ans: Q.4 A force of (3 ˆi 1.5ˆj) N acts on a 5 kg body. The body is at a position of (2 ˆi  3ˆj) m and is travelling at 4 ms–1. The force acts on the body until it is at the position (ˆi  5ˆj) m. Assuming no other force does work on the body, find the final speed of the body. Ans: Q.5 A particle of mass m is moving in a straight line under the influence of conservative force such that its velocity v varies with displacement x from a fixed point as v2 =  – x2 where  and  are constants. Considering that fixed point as reference for zero potential energy, find the total mechanical energyof the particle at any instant t. Ans: Q.6 A car begins from rest at time t = 0 and then accelerates along a straight track during the interval 0 < t  2s and thereafter with constant velocity as shown in the graph. Acoin is initially at rest on the floor of the car. At t = 1 s, the coin begins to slip. Find the coefficient of static friction between the floor and the coin. [Fact: Equation of a parabola having vertex at origin and which opens up is y = kx2] Ans: μs = Q.7 Asmall block of mass 2m initially rests at the bottom ofa circular, vertical track, which has a radius of R. The contact surface between the mass and the loop is frictionless. Abullet ofmass mstrikes the block horizontally with initial speed v0 and remain embedded in the block as the block and the bullet circle the loop. Determine each of the following in terms of m, v0, R and g. (a) The speed of the masses immediately after the impact. (b) The minimum initial speed of the bullet if the block and the bullet are to successfully execute a complete ride on the loop. Ans: (a) (b) Q.8 Two massless strings of same length hang from the ceiling very near to each other as shown in the figure. Two balls A and B of masses 0.25 kg and 0.5 kg are attached to the string. The ballAis released from rest at a height as shown in the figure, so that its velocity is 3 m/s before collision. The collision between two balls is completely elastic. Find the velocity of ball Ajust after the collision. Ans: vA = Q.9 A particle moves along a circle of constant radius with radial acceleration changing with time as ar = k tn where k is constant and n > 1. How does the power developed by the net force on the particle vary with time? Ans: Q.10 Indian government sends Chunnu (45 kg) and Munnu (45 kg) to outer space where there is no gravity.One day both of them come out of the spaceship to play game of catch. Chunnu throws a ball of mass m = 5 kg to Munnu. If the ball has a horizontal velocity of 5 m/s as seen by Chunnu himself. What is Chunnu's velocity after the ball leaves his hand? Ans: Q.11 The mass center of the homogeneous plate shown in the figure is in point A. What is the ratio b/a? Ans: b/a = Q.12 Two different masses are connected to two light and inextensible strings as shown in the figure. Both masses rotate about a central fixed point with constant angular speed of 10 rad s–1in horizontal plane. Find the ratio T1 of tensions in the strings. 2 T Ans: 1 = T2 Q.13 A small ball is projected from point P on floor towards a wall as shown. It hits the wall when its velocity is horizontal. Ball reaches point P after one bounce on the floor. If the coefficient of restitution is the same for the two collisions, find its value. [All surfaces are smooth] Ans: e = Q.14 Block 1 sits on top of block 2. Both of them have a mass of 1 kg. The coefficients of friction between blocks 1 and 2 are s = 0.75 and k = 0.60. The table is frictionless. A force P/2 is applied on block 1 to the left, and force P on block 2 to the right. Find the minimum value of P such that both blocks move relative to each other. Ans: Pmin = Q.15 You are standing at the top of a ladder of length 𝑙. Your mass is M, the ladder is inclined at an angle  with respect to the horizontal, and the mass of the ladder is negligible. Assume that there is no friction between the ladder and the smooth wall. (a) Draw Free body diagram of ladder. (b) Derive an expression for the minimum coefficient of friction between the ladder and the ground required to ensure that ladder does not slip . Ans: min = Q.16 A bicycle wheelof radius R and mass m is initially spinning with angular velocity  about its centre. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to move forward until it begins to roll without slipping with an unknown final angular velocity  and an unknown velocity of the center of mass vcm, f.. Assume that all the mass of the wheel is located on the rim. (a) Draw a free body diagram of all the forces acting on the bicycle wheel while it is moving forward, before it starts pure rolling. (b) What is the relation between the angular velocity of the wheel  and the velocity of the center of mass vcm, f.when it begins to roll without slipping? (c) Calculate the velocity of the center of mass of the wheel (vcm, f.) when it begins to roll without slipping in terms of  , R ? Ans: (b) = (c) = Q.17(a) In the figure shown a uniform semicircular disc of radius R and mass m can rotate about a horizontal fixed smooth axis AB. Initially the plane of the disc is horizontal. It is released from there. Find the angular acceleration just after release.(Use the fact that for semicircular disc, centre of mass would be 4R at distance 3 frm AB) (b) if a circular hole of radius R/2 is removed from same semicircular disc as shown find the moment of inertia about AB of the remaining body, Ans: (a) = (b) = Q.18 The graph shown in the figure represents change in temperature of 5 kg of a substance as it absorbs heat at a constant rate of 42 kJ min–1. Find the latent heat of vapourization of the substance. Ans: Lf = Q.19 A bobbin of mass m and moment of inertia I relative to its own axis is being pulled towards right along a horizontal surface by the light string tightly wrapped as shown in figure. There is no slipping on the surface throughout the motion. (a) If string is pulled by horizontal velocity V, then find the angular velocity of bobbin. (b) If string is pulled by horizontal acceleration a, then find the tension in string. Ans: (a) ω = (b) T = Q.20 A glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is 300 cm3, then find the volume of the flask. [Given that coefficient of volume expansion of mercury and coefficient of linear expansion of glass are 1.8 × 10–4 (°C)–1 and 9 × 10–6 (°C)–1 respectively] Ans: Vflask = EXTRA PAGE