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Physics · LAWS OF MOTION
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Physics · LAWS OF MOTION
A cyclist turns on an unbanked circular track of radius \( R = 16\text{ m} \) at a speed of \( v = 36\text{ km/h} \). Taking \( g = 10\text{ m/s}^2 \), the minimum coefficient of static friction needed to negotiate the turn safely is \( \mu_{s1} \). If the road becomes wet such that the coefficient of static friction reduces to \( \mu_{s2} = 0.25 \), what will be the new maximum safe speed \( v_2 \)?
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Two identical billiard balls of mass \( m \) collide with a rigid wall at the same speed \( v \). Ball A strikes the wall normally and rebounds with the same speed. Ball B strikes the wall at an angle of \( 45^\circ \) to the normal and reflects elastically at the same angle with unchanged speed. What is the ratio of the magnitude of impulse imparted by the wall to ball A to that imparted to ball B?
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In a trolley and block system, a block of mass \( 3\text{ kg} \) hangs vertically and is connected by a light inextensible string passing over an ideal pulley to a trolley of mass \( 20\text{ kg} \) moving on a horizontal track. The coefficient of kinetic friction between the trolley and the track is \( \mu_k = 0.04 \). Calculate the tension \( T \) in the connecting string. (Take \( g = 10\text{ m s}^{-2} \))
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A block of mass \( 5\text{ kg} \) is pulled along a rough horizontal surface by a force \( F = 25\text{ N} \) applied at an angle \( \theta = 37^\circ \) above the horizontal (\( \cos 37^\circ = 0.8, \sin 37^\circ = 0.6 \)). If the coefficient of kinetic friction between the block and floor is \( \mu_k = 0.2 \) and \( g = 10\text{ m/s}^2 \), the acceleration of the block is:
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Refer to the given figure showing a stone being whirled in a horizontal circle at constant speed by a person holding a string. The direction of the net external force acting on the stone at any instant is:
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A bullet of mass \( 20\text{ g} \) is fired horizontally from a gun of mass \( 4\text{ kg} \) with a velocity of \( 400\text{ m s}^{-1} \). The recoil velocity of the gun is:
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In the block and trolley system shown in the figure, a trolley of mass \( 20\text{ kg} \) on a rough horizontal table is connected by a light string passing over a frictionless pulley to a hanging block of mass \( 3\text{ kg} \). The coefficient of kinetic friction between the trolley and the surface is \( \mu_k = 0.04 \). Taking \( g = 10\text{ m/s}^2 \), the tension \( T \) in the string while the system is accelerating is:
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A block placed on an inclined plane just begins to slide down when the angle of inclination is \( 30^\circ \). If the angle of inclination of the plane is increased to \( 45^\circ \), assuming \( \mu_k \approx \mu_s \), the acceleration of the block down the incline will be (take \( g = 10\text{ m/s}^2 \)):
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A stone of mass \( 0.2 \text{ kg} \) tied to the end of a string is whirled in a horizontal circle of radius \( 0.5 \text{ m} \) with a constant speed of \( 4 \text{ m s}^{-1} \). The tension force provided by the string is:
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A variable force \( F = (10 + 2t)\text{ N} \) acts on a particle of mass \( 2\text{ kg} \) initially at rest over a time interval from \( t = 0 \) to \( t = 4\text{ s} \). The net change in momentum of the particle during this interval is:
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The vertical displacement of a particle of mass \( 0.5\text{ kg} \) moving under gravity and variable resistive forces is given by \( y(t) = 5 t + 3 t^2 - t^3 \) (where \( y \) is in meters and \( t \) in seconds). The net vertical force acting on the particle at time \( t = 2\text{ s} \) has a magnitude of:
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A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \( 12\text{ m s}^{-1} \). If the mass of the ball is \( 0.15\text{ kg} \), determine the magnitude of the impulse imparted to the ball.
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A block of mass \( m = 5\text{ kg} \) is placed on an inclined plane of inclination \( \theta = 37^\circ \) (\( \sin 37^\circ = 0.6, \cos 37^\circ = 0.8 \)). The coefficient of static friction is \( \mu_s = 0.5 \) and kinetic friction is \( \mu_k = 0.4 \). Taking \( g = 10\text{ m/s}^2 \), determine whether the block remains at rest or slides down, and find the net force acting on the block along the incline.
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A time-dependent force \( \vec{F} = (6 t \hat{i} + 4 t^2 \hat{j})\text{ N} \) acts on a particle of mass \( 2\text{ kg} \) which is initially at rest at \( t = 0 \). The speed of the particle at \( t = 3\text{ s} \) is:
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A batsman hits back a ball of mass \( m \) moving with speed \( v \) straight in the direction of the bowler without changing its speed. The contact time between the bat and the ball is \( \Delta t \). In a second situation, the mass of the ball is doubled, its speed is increased by 50%, and the duration of contact is reduced to half. What is the ratio of the average force exerted on the ball in the second situation to that in the first situation?
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A block of mass \( 4\text{ kg} \) is kept on the floor of an elevator which is accelerating upwards with a constant acceleration of \( 2.5\text{ m/s}^2 \). Taking \( g = 10\text{ m/s}^2 \), the normal reaction force exerted by the elevator floor on the block is:
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Match List-I with List-II regarding forces and equilibrium conditions: List-I List-II A Two concurrent forces in equilibrium I \( \mathbf{F}_1 + \mathbf{F}_2 + \mathbf{F}_3 = 0 \) B Three concurrent forces in equilibrium II \( \mathbf{p}_A + \mathbf{p}_B = \mathbf{p}'_A + \mathbf{p}'_B \) C Conservation of linear momentum III \( \mathbf{F}_{AB} = -\mathbf{F}_{BA} \) D Newton's third law of motion IV \( \mathbf{F}_1 = -\mathbf{F}_2 \) Choose the correct answer from the options given below:
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The linear momentum \( p \) of a body moving along a straight line varies with time \( t \) according to \( p(t) = (3t^2 + 4t + 2) \text{ kg m s}^{-1} \). The magnitude of force acting on the body at time \( t = 2 \text{ s} \) is:
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Match the device/method in List-I with its physical application in List-II: List-I List-II A Ball bearings I Reduces friction between moving parts in machines B Thin cushion of air II Maintained between solid surfaces in relative motion C Lubricants III Used to reduce kinetic friction in sliding machine parts D Tyres on road IV Provides necessary external force to accelerate car Choose the correct answer from the options given below:
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A cricket ball of mass \( m = 150\text{ g} \) moving with a speed of \( v = 20\text{ m/s} \) is caught by a player. If the player stops the ball in \( \Delta t_1 = 0.1\text{ s} \), average force \( F_1 \) is exerted. If the player pulls his hands back extending the stopping time to \( \Delta t_2 = 0.4\text{ s} \), average force \( F_2 \) is exerted. Find \( F_2 \) and \( F_1 \) respectively.
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Given below are two statements: Statement I: The second law of motion is a local relation, meaning that the force \( \mathbf{F} \) at a point in space at a certain instant of time is related to the acceleration \( \mathbf{a} \) at that same point at that same instant. Statement II: The acceleration of a particle at any given instant depends significantly on the previous motion or history of the particle prior to that instant. In the light of the above statements, choose the most appropriate answer from the options given below:
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Given below are two statements: Statement I: The maximum value of static friction \( (f_s)_{\text{max}} \) is independent of the area of contact between surfaces. Statement II: The coefficient of kinetic friction \( \mu_k \) is generally slightly greater than the coefficient of static friction \( \mu_s \). In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · LAWS OF MOTION
