Friction PYQs Set 6 (PDF)

Set 6 of 7 · Questions 151-180 of 182

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Mere Teacher · Previous Year Questions JEE Main Physics · Friction · Set 6 (Q151-180)
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151. $All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :$ (1) $g$ (2) $\frac{g}{3}$ (3) $\frac{g}{2}$ (4) $\frac{g}{4}$ 152. $At the moment t = 0, a time dependent force F = at (where a is constant equal to 1 Ns^{- 1}) is applied to a body of mass 1 kg resting on a smooth horizontal plane as shown in the figure. If the direction of this force makes an angle 45^{\circ} with the horizontal, then the velocity of the body at the moment it leaves the plane is (acceleration due to gravity = 10 m s^{- 2})$ (1) $50 ms^{- 1}$ (2) $502 r$ (3) $1002 ms^{- 1}$ (4) $100 ms^{- 1}$ 153. $A car is negotiating a curved road of radius R. The road is banked at an angle θ . The coefficient of friction between the tyres of the car and the road is μ_{s} . The maximum safe velocity on this road is$ (1) $\frac{g}{R} \frac{μ _{s} + t a n Θ}{1 - μ _{s} t a n Θ}$ (2) $\frac{g}{R ^{2}} \frac{μ _{s} + t a n Θ}{1 - μ _{s} t a n Θ}$ (3) $g R^{2} \frac{μ _{s} + t a n Θ}{1 - μ _{s} t a n Θ}$ (4) $g R \frac{μ _{s} + t a n Θ}{1 - μ _{s} t a n Θ}$ 154. $A block of mass m_{1} = 1 kg and another mass m_{2} = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination θ. Various values of θ are given in List I. The coefficient of friction between the block m_{1} and the plane is always zero. The coefficient of static and dynamic friction between the block m_{2} and the plane are equal to µ = 0.3. In List II expression for the friction on block m_{2} given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g. List-I (P) θ = 5^{\circ} (Q) θ = 10^{\circ} (R) θ = 15^{\circ} (S) θ = 20^{\circ} List-II (1) m_{2} g sin θ (2) (m_{1} + m_{2}) g sin θ (3) μ m_{2} g cos θ (4) μ (m_{1} + m_{2}) g cos θ Code:$ (1) $P-1, Q-1, R-1, S-3$ (2) $P-2, Q-2, R-2, S-3$ (3) $P-2, Q-2, R-2, S-4$ (4) $P-2, Q-2, R-3, S-3$ 155. $The following is not the method of reducing friction$ (1) $using ball bearings$ (2) $applying grease$ (3) $applying paint$ (4) $forming a thin air cushion$ 156. $A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial position with respect to the table, the ball (1) remains stationary if there is no friction between the paper and the ball. (2) moves to the left and starts rolling backwards, i.e. to the left if there is a friction between the paper and the ball. (3) moves forward, i.e. in the direction in which the paper is pulled. Here, the correct statement/s is/are$ (1) $both (1) and (2)$ (2) $only (3)$ (3) $only (1)$ (4) $only (2)$ 157. $Three blocks are arranged as shown in which ABCD is a horizontal plane. Strings are massless and both pulley stands vertical while the strings connecting blocks m_{1} and m_{2} are also vertical and are perpendicular to faces AB and BC which are mutually perpendicular to each other. If m_{1} and m_{2} are 3 kg and 4 kg respectively. Coefficient of friction between the block m_{3} = 10 kg and surface is µ = 0.6 then, frictional force on m_{3} is -$ (1) $30 N$ (2) $40 N$ (3) $50 N$ (4) $60 N$ 158. $An iron block of sides 50 cm \times 8 cm \times15 cm has to be pushed along the floor. The force required will be minimum when the surface in contact with ground is:$ (1) $8 cm \times 15 cm surface$ (2) $50 cm \times 15 cm surface$ (3) $8 cm \times 50 cm surface$ (4) $Force is same for all surfaces$ 159. $A block of mass m = 2 kg is initially at rest on a horizontal surface. A horizontal force F_{1} = (6 N) i and a vertical force F_{2} = (10 N) j are then applied to the block. The coefficients of static friction and kinetic friction for the block and the surfaces are 0.4 and 0.25 , respectively. The magnitude of the frictional force acting on the block is (assume, g = 10 m / s^{2})$ (1) $2.5 N$ (2) $4.0 N$ (3) $3.3 N$ (4) $3.0 N$ 160. $In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25 . The value of m, for which M = 10 kg will move down with an acceleration of 2 m / s^{2}, is : (take g = 10 m / s^{2} and (tan 37^{\circ} = 3/4)$ (1) $9 kg$ (2) $4.5 kg$ (3) $6.5 kg$ (4) $2.25 kg$ 161. $Consider a system of blocks X, A and B as shown in the figure. The blocks A and B have equal mass and are connected by a massless string through a massless pully. The coefficient of friction between block A and X or B and X is 0.5 . If block X moves on the horizontal frictionless surface what should be its minimum acceleration such that blocks A and B remain stationary. (g = acceleration due to gravity.)$ (1) $\frac{g}{3}$ (2) $3 g$ (3) $\frac{g}{4}$ (4) $3 g 4$ 162. $An inclined plane making an angle of 30^{\circ} with horizontal is placed in a uniform horizontal electric field 200 N/C as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m . If the coefficient of frication is 0.2, find the time taken by the body to reach the bottom. (g = 9.8 m / s^{2}, sin 30^{\circ} = \frac{1}{2}; cos 30^{\circ} = \frac{3}{2})$ (1) $2.3 s$ (2) $0.46 s$ (3) $1.3 s$ (4) $0.92 s$ 163. $A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration a_{0} . The angle between the inclined plane and ground is θ and its base length is L . Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is____.$ (1) $\frac{2 L}{gsinθ - a _{0} cosθ}$ (2) $\frac{4 L}{g cos ^{2} θ - a _{0} sinθcosθ}$ (3) $\frac{2 L}{gsin 2 θ - a _{0} ( 1 + cos 2 θ )}$ (4) $\frac{4 L}{gsin 2 θ - a _{0} ( 1 + cos 2 θ )}$ 164. $A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is$ (1) $2 N$ (2) $20 N$ (3) $50 N$ (4) $100 N$ 165. $One end of a massless spring of spring constant k and natural length l_{0} is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity ω about an axis passing through fixed end, then the elongation of the spring will be:$ (1) $\frac{k - m ω ^{2} l _{0}}{m ω ^{2}}$ (2) $\frac{m ω ^{2} l _{0}}{k + m ω ^{2}}$ (3) $\frac{m ω ^{2} l _{0}}{k - m ω ^{2}}$ (4) $\frac{k + m ω ^{2} l _{0}}{m ω ^{2}}$ 166. $Three blocks are arranged as shown. ABCD is the horizontal plane. Strings are massless and both pulleys stands vertical while the strings connecting blocks m_{1} and m_{2} are also vertical and perpendicular to each other. The masses m_{1} and m_{2} are 3 kg and 4 kg respectively. Coefficient of friction between the block m_{3} = 10 kg and surface is µ = 0.6, then -$ (1) $The system of blocks can be in equilibrium$ (2) $At equilibrium frictional force on block m_{3} is 60 N$ (3) $At equilibrium frictional force on block m_{3} is 50 N$ (4) $Total force applied by surface on block m_{3} is 50 5 N$ 167. $A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be:$ (1) $9.8N$ (2) $39.2N$ (3) $49N$ (4) $78.4N$ 168. $The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient of kinetic friction between the object and the incline plane is$ (1) $\frac{1}{1 - n ^{2}}$ (2) $1 - \frac{1}{n ^{2}}$ (3) $1 + \frac{1}{n ^{2}}$ (4) $1 - \frac{1}{n ^{2}}$ 169. $A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ' a^{1} will be:$ (1) $\frac{g}{4}$ (2) $\frac{g}{2}$ (3) $\frac{3 g}{4}$ (4) $g$ 170. $A body of mass 10 kg is kept on a horizontal surface. The coefficient of kinetic friction between the body and the surface is 0.5 . A horizontal force of 60 N is applied on the body. The resulting acceleration of the body is about$ (1) $1 m s^{- 2}$ (2) $5 m s^{- 2}$ (3) $6 m s^{- 2}$ (4) $zero$ 171. $The weight of an aeroplane flying in the air is balanced by$ (1) $Vertical component of the thrust created by air currents striking the lower surface of the wings$ (2) $Force due to reaction of gases ejected by the revolving propeller$ (3) $Up thrust of the air which will be equal to the weight of the air having the same volume as the plane$ (4) $Force due to the pressure difference between the upper and lower surfaces of the wings created by different air speeds on the surfaces$ 172. $A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length 'L-l' is hanging on the other side of the pulley. At a certain point of time, when l = \frac{L}{x}, the acceleration of the chain is \frac{g}{2} . The value of x is .........$ (1) $6$ (2) $2$ (3) $1.5$ (4) $4$ 173. $A body of mass 'm' is launched up on a rough inclined plane making an angle of 3 0^{0} with the horizontal. The coefficient of friction between the body and plane is \frac{x}{5} if the time of ascent is half of the time of descent. The value of x is$ 174. $Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is \frac{3}{7} . Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is_______N . (Round off to the Nearest Integer) [Take g as (9.8 ms^{- 2})$ 175. $As shown in the figure, a block of mass 3 kg is kept on a horizontal rough surface of coefficient of friction \frac{1}{3 3} . The critical force to be applied on the vertical surface as shown at an angle 60^{\circ} with horizontal such that it does not move, will be 3 x . The value of x will be (g = 10 m / s^{2}; sin 60^{\circ} = \frac{3}{2}; cos 60^{\circ} = \frac{1}{2}) (round off tonearest integer)$ 176. $A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is \frac{x}{5} Mg for x =_________. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)$ 177. $The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is \dots..N. (take g = 10 m s^{- 2})$ 178. $A boy of mass 4 kg is standing on a piece of wood having mass 5 kg . If the coefficient of friction between the wood and the floor is 0.5,the maximum force that the boy can exert onthe rope so that the piece of wood does notmove from its place is N . (Round off to the Nearest Integer) [Take (g = 10 ms^{- 2})$ 179. $When a body slides down from rest along a smooth inclined plane making an angle 3 0^{0} with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time α T, where α is a constant greater than 1. The co-efficient of friction between the body and the rough plane is \frac{1}{x} (1 - \frac{1}{α ^{2}}) where x =......$ 180. $A car is moving on a plane inclined at 3 0^{0} to the horizontal with an acceleration of 10 m s^{- 2} parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take g = 10 m s^{- 2})$