Newton's Laws of Motion PYQs Set 4 (PDF)

Set 4 of 7 · Questions 91-120 of 197

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Mere Teacher · Previous Year Questions JEE Main Physics · Newton's Laws of Motion · Set 4 (Q91-120)
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91. $A cyclist is riding with a speed of 36 km / h . As he approaches a circular turn on the road of radius 50 m, he applies brakes and reduces his speed at the constant rate of 0.5 m / s every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are$ (1) $\frac{3}{2} m / s^{2}, tan^{- 1} (4)$ (2) $\frac{3}{2} m / s^{2}, tan^{- 1} (\frac{1}{4})$ (3) $17 m / s^{2}, tan^{- 1} (\frac{1}{4})$ (4) $\frac{17}{2} m / s^{2}, tan^{- 1} (4)$ 92. $Two rectangular blocks of masses 40 kg and 60 kg are connected by a string and kept on a frictionless horizontal table. If a force of 1000 N is applied on 60 kg block away from 40 kg block, then the tension in string is$ (1) $450 N$ (2) $400 N$ (3) $350 N$ (4) $500 N$ 93. $The position vector of a particle related to time t is given by r = (10 t i + 15 t^{2} j + 7 k) m . The direction of net force experienced by the particle is:$ (1) $Positive x-axis$ (2) $In x - y plane$ (3) $Positive y-axis$ (4) $Positive z-axis$ 94. $A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of a . The pendulum will tilt [NEET 2020]$ (1) $to the left and the angle of inclination of the pendulum with the vertical is sin^{- 1} (\frac{g}{a})$ (2) $to the left and angle of inclination of the pendulum with the vertical is tan^{- 1} (\frac{a}{g})$ (3) $to the left and angle of inclination of the pendulum with the vertical is sin^{- 1} (\frac{a}{g})$ (4) $to the left and angle of inclination of the pendulum with the vertical is tan^{- 1} (\frac{g}{a})$ 95. $A mass M is suspended by a rope from a rigid support at P as shown in the figure. Another rope is tied at the end Q, and it is pulled horizontally with a force F. If the rope PQ makes angle θ with the vertical then the tension in the string PQ is$ (1) $F s in θ$ (2) $F / s in θ$ (3) $F cos θ$ (4) $F / cos θ$ 96. $Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:$ (1) $40N$ (2) $5N$ (3) $20N$ (4) $10N$ 97. $A stone is dropped from a height h . It hits the ground with a certain momentum P . If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by$ (1) $68%$ (2) $41%$ (3) $200%$ (4) $100%$ 98. $Two masses M_{1} and M_{2} are arranged as shown in the figure. Let ' a' be the magnitude of the acceleration of the mass M_{1} . If the mass of M_{1} is doubled and that of M_{2} is halved, then the acceleration of the system is (Treat all surfaces as smooth; masses of pulley and rope are negligible)$ (1) $(\frac{M _{1} + M _{2}}{4 M _{1} + M _{2}}) a$ (2) $(\frac{2 M _{1} + M _{2}}{4 M _{1} + M _{2}}) a$ (3) $(\frac{M _{1} + 2 M _{2}}{4 M _{1} + 2 M _{2}}) a$ (4) $(\frac{M _{1} + 2 M _{2}}{M _{1} + M _{2}}) a$ 99. $A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions T_{1} and T_{2}, respectively, are (in N): (Take acceleration due to gravity 10 m / s^{2})$ (1) $53, 5$ (2) $53, 53$ (3) $5,5$ (4) $5, 53$ 100. $A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of 60 ° with the vertical. The new reading of the balance is$ (1) $103 kg wt$ (2) $203 kgwt$ (3) $20 kgwt$ (4) $10 kgwt$ 101. $A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is [NEET 2018]$ (1) $a = g cos θ$ (2) $a = \frac{g}{sin θ}$ (3) $a = \frac{g}{cosec θ}$ (4) $a = g tanθ$ 102. $A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R ?$ (1) (2) (3) (4) 103. $A roller coaster is designed such that riders experience “weightlessness” as they go around the top of a hill whose radius of curvature is 20 m . Re speed of the car at the top of the hill is between$ (1) $16 m / s and 17 m / s$ (2) $13 m / s and 14 m / s$ (3) $14 m / s and 15 m / s$ (4) $15 m / s and 16 m / s$ 104. $A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 ms^{- 2} . The action force of the system on the floor is equal to$ (1) $297 N$ (2) $291 N$ (3) $196 N$ (4) $294 N$ 105. $A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 m/ s^{2} . What would be the reading on the scale? (g = 10 m / s^{2})$ (1) $zero$ (2) $400 N$ (3) $800 N$ (4) $1200 N$ 106. $A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should the lift be accelerated upwards in order to reduce its period to T /2 ? (g is acceleration due to gravity).$ (1) $4g$ (2) $g$ (3) $2g$ (4) $3g$ 107. $A sphere of mass ' m' moving with velocity ' v' collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)$ (1) $\frac{e - 1}{2}$ (2) $\frac{e}{2}$ (3) $\frac{e + 1}{2}$ (4) $e$ 108. $Two masses of 5 kg and 3 kg are suspended with the help of massless inextensible strings as shown in figure. When whole system is going upwards with acceleration 2 m / s^{2}, the value of T_{1} is (use g = 9.8 m / s^{2})$ (1) $23.6 N$ (2) $94.4 N$ (3) $59 N$ (4) $35.4 N$ 109. $A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' F' is applied at the mid point of the rope so that the rope makes an angle of 45^{\circ} with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and g = 10 m / s^{2})$ (1) $10 N$ (2) $\frac{10}{2} N$ (3) $1 N$ (4) $\frac{1}{10 \times 2} N$ 110. $The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is$ (1) $6 0^{0}$ (2) $12 0^{0}$ (3) $15 0^{0}$ (4) $9 0^{0}$ 111. $At any instant the velocity of a particle of mass 500 g is (2 t i + 3 t^{2} j) m s^{- 1} . If the force acting on the particle at t = 1 s is (i + x j) N . Then the value of x will be:$ (1) $3$ (2) $4$ (3) $2$ (4) $6$ 112. $A balloon and its content having mass M is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be (Take ' g' as acceleration due to gravity)$ (1) $\frac{3 Ma}{2 a + g}$ (2) $\frac{2 Ma}{3 a + g}$ (3) $\frac{3 Ma}{2 a - g}$ (4) $\frac{2 Ma}{3 a - g}$ 113. $The figure shows the position - time (x - t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is$ (1) $0.4 Ns$ (2) $0.8 Ns$ (3) $1.6 Ns$ (4) $0.2 Ns$ 114. $The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to be under equilibrium, the angle θ should be$ (1) $0^{0}$ (2) $3 0^{0}$ (3) $4 5^{0}$ (4) $6 0^{0}$ 115. $A block is kept on a frictionless inclined surface with angle of inclination 'α'. The incline is given an acceleration 'a' to keep the block stationary. Then a is equal to$ (1) $g$ (2) $g tan α$ (3) $g / tan α$ (4) $g cosec α$ 116. $A particle of mass m is fixed to one end of light spring having force constant k and unstretched length l_{o} . The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:$ (1) $\frac{l _{0} m ω ^{2}}{k - m ω ^{2}}$ (2) $\frac{l _{0} m ω ^{2}}{k + m ω ^{2}}$ (3) $\frac{l _{0} m ω ^{2}}{k - mω}$ (4) $\frac{l _{0} m ω ^{2}}{k + mω}$ 117. $A bird is sitting on stretched telephone wires. If its weight is W then the additional tension produced by it in the wires will be$ (1) $T = W$ (2) $T>W$ (3) $T<W$ (4) $T = 0$ 118. $A stone is projected vertically upwards with speed v Another stone of same mass is projected at an angle of 60^{\circ} with the vertical with the same speed v' The ratio of their potential energies at the highest points of their journey is (sin 30^{\circ} = cos 60^{\circ} = 0.5, cos 30^{\circ} = sin 60^{\circ} = 3 /2)]$ (1) $4 : 1$ (2) $3 : 2$ (3) $2 : 1$ (4) $1 : 1$ 119. $A mass of l kg is suspended by a thread. It is (i) lifted up with an acceleration 4.9 m / s^{2}, (ii) lowered with an acceleration 4.9 m / s^{2} . The ratio of the tensions is$ (1) $1 : 3$ (2) $1 : 2$ (3) $3 : 1$ (4) $2 : 1$ 120. $A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7^{t h} and 8^{t h} ball is\dots.N when 6^{t h} ball just leaves the$