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Physics · LAWS OF MOTION
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Physics · LAWS OF MOTION
Given below are two statements: Statement I: The law of conservation of linear momentum is a direct fundamental consequence of Newton's second and third laws of motion applied to an isolated system. Statement II: In an inelastic collision between two colliding bodies, the total kinetic energy of the system is conserved, but the total linear momentum is not conserved. In the light of the above statements, choose the most appropriate answer from the options given below:
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In the given diagram, a girl whirls a stone tied to a string in a horizontal circle at a constant speed \( v \). If the string breaks suddenly at the point shown, what will be the immediate trajectory of the stone relative to the ground, viewed from directly above?
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Refer to the given figure showing a block of mass \( 4\text{ kg} \) on an inclined plane at angle \( \theta \). What are the components of the gravitational force \( mg \) parallel and perpendicular to the inclined plane respectively?
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A rubber ball of mass \( 0.15\text{ kg} \) is dropped from a height of \( 5\text{ m} \) onto a hard floor. It rebounds upwards to a maximum height of \( 3.2\text{ m} \). If the time of collision with the floor is \( 0.03\text{ s} \) and \( g = 10\text{ m/s}^2 \), the average normal force exerted by the floor on the ball during the impact is:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When a stationary bus starts accelerating suddenly, passengers standing inside are thrown backwards relative to the bus. Reason (R): Due to inertia of rest, the upper part of the passenger's body tends to remain in its initial position while the feet in contact with the floor move forward with the bus. In the light of the above statements, choose the correct answer from the options given below:
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A stream of water flowing horizontally at a speed of \( 15\text{ m/s} \) pushes against a rigid vertical wall at a steady rate of mass flow equal to \( 20\text{ kg/s} \). Assuming the water comes to rest immediately after striking the wall without rebounding, the force exerted by the water stream on the wall is:
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A block of mass \( m = 4\text{ kg} \) is projected with an initial velocity \( v_0 = 10\text{ m/s} \) along a rough horizontal plane. The block comes to rest after covering a distance of \( d = 25\text{ m} \). Taking \( g = 10\text{ m/s}^2 \), calculate the coefficient of kinetic friction \( \mu_k \) and the rate of work done by friction (power) at time \( t = 1\text{ s} \).
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A body of mass \( m = 3\text{ kg} \) moves under the influence of a time-dependent force such that its position vector is given by \( \mathbf{r}(t) = (t^3 \hat{i} + 2t^2 \hat{j} - t \hat{k})\text{ m} \). Determine the magnitude of the net force acting on the body at \( t = 1\text{ s} \) and the magnitude of the impulse delivered to the body during the time interval from \( t = 0\text{ s} \) to \( t = 1\text{ s} \).
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A machine gun fires bullets of mass \( 40\text{ g} \) each with a muzzle speed of \( 1200\text{ m/s} \). If the gunman can exert a maximum holding force of \( 144\text{ N} \) on the gun to prevent it from moving backward, the maximum rate at which bullets can be fired per second is:
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A loaded truck of mass \( 4000 \text{ kg} \) and a light car of mass \( 1000 \text{ kg} \) have the same linear momentum. If the speed of the light car is \( 24 \text{ m s}^{-1} \), the speed of the loaded truck is:
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Given below are statements regarding Newton's laws of motion: (A) If the net external force acting on a body is zero, its acceleration must be zero. (B) Any internal forces in a system of particles can alter the acceleration of the center of mass of the system. (C) Force is required to continuously change the direction of velocity even when the speed of a body remains constant. (D) Newton's second law is consistent with the first law when the net external force is set to zero. Choose the correct answer from the options given below:
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A block of mass \( m \) is pulled along a horizontal rough surface (\( \mu_s \)) by a horizontal force \( F \). The normal force exerted by the surface on the block is:
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Refer to the given figure showing two collisions of a ball with a wall. In case (b), the angle made by the path of the ball with the normal is \( 30^\circ \). What is the y-component of the impulse delivered to the ball in case (b)?
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Match List-I with List-II: List-I List-II A Aristotle's Fallacy I External force required continuously for motion (flawed) B Galileo's Law of Inertia II Body continues uniform motion if net external force is zero C Horizontal motion of projectile III Horizontal velocity component remains unchanged D Stone released from accelerated train IV Zero horizontal acceleration immediately after release Choose the correct answer from the options given below:
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A stone of mass \( 0.4\text{ kg} \) is tied to a light inextensible string of length \( 0.9\text{ m} \) and whirled in a horizontal circle on a smooth table top. If the string can withstand a maximum tension of \( 100\text{ N} \), the maximum linear speed with which the stone can be rotated without breaking the string is:
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A book of mass \( 1.5 \text{ kg} \) rests on a smooth horizontal table. Taking \( g = 9.8 \text{ m s}^{-2} \), what is the magnitude of the normal reaction force exerted by the table on the book?
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A mass rests on a horizontal plane. The plane is gradually inclined until at an angle \( \theta = 15^\circ \) with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?
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Three concurrent forces \( \mathbf{F}_1 \), \( \mathbf{F}_2 \), and \( \mathbf{F}_3 \) keep a particle in equilibrium. If \( \mathbf{F}_1 = 3\hat{i} - 4\hat{j}\text{ N} \) and \( \mathbf{F}_2 = -2\hat{i} + 6\hat{j}\text{ N} \), then the third force \( \mathbf{F}_3 \) is equal to:
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A train is moving along a straight horizontal track with an acceleration of \( 2 \text{ m s}^{-2} \). At the moment when its velocity is \( 10 \text{ m s}^{-1} \), a stone of mass \( 0.5 \text{ kg} \) is dropped from a window. Taking \( g = 10 \text{ m s}^{-2} \), the net force acting on the stone immediately after release is:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): To calculate the acceleration of a single body in a system, both action and reaction forces acting on that body must be added to give the net force. Reason (R): Action and reaction forces act simultaneously on two different bodies and never cancel each other on a single body. In the light of the above statements, choose the correct answer from the options given below:
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A block of mass \( 5\text{ kg} \) rests on a rough horizontal surface with coefficients of static friction \( \mu_s = 0.4 \) and kinetic friction \( \mu_k = 0.3 \). A horizontal pulling force of \( 15\text{ N} \) is applied to the block. Taking \( g = 10\text{ m/s}^2 \), the magnitude of the frictional force exerted by the surface on the block is:
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Match List-I (Physical Quantity) with List-II (Definition / Formula): List-I List-II A Momentum (\( \mathbf{p} \)) I Net external force (\( \mathbf{F} \)) B Time derivative of momentum (\( d\mathbf{p}/dt \)) II Zero acceleration C Impulse III Product of mass and velocity (\( m\mathbf{v} \)) D Net force zero (\( \mathbf{F} = 0 \)) IV Change in momentum (\( \Delta \mathbf{p} \)) Choose the correct answer from the options given below:
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