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Physics · LAWS OF MOTION
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Physics · LAWS OF MOTION
A spring of force constant \( k = 200\text{ N m}^{-1} \) is stretched by an external force by an elongation \( x = 0.05\text{ m} \). The magnitude of restoring force generated in the spring is:
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A car moves along a banked circular road of radius \( R \) inclined at an angle \( \theta \) with the horizontal. If the coefficient of static friction between the tyres and the road is \( \mu_s \) (where \( \mu_s < \tan\theta \)), which of the following expressions gives the minimum speed \( v_{\min} \) required to prevent the car from sliding down the slope?
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The ratio of rolling friction force \( f_r \) to kinetic sliding friction force \( f_k \) for a rigid circular wheel rolling on a solid surface is approximately of the order of:
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A body of mass \( 2\text{ kg} \) changes its velocity vector from \( \mathbf{v}_1 = 3\hat{i} + 4\hat{j}\text{ m s}^{-1} \) to \( \mathbf{v}_2 = -3\hat{i} + 4\hat{j}\text{ m s}^{-1} \). The magnitude of the impulse imparted to the body is:
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Determine the maximum acceleration of a train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and the train's floor is \( 0.15 \). (Take \( g = 10\text{ m s}^{-2} \))
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A body of mass \( m \) is connected between two identical light springs, each of spring constant \( k \), arranged in parallel on a horizontal frictionless table. If the body is pulled horizontally so that the system experiences a total stretch of \( x \), the work done against the net restoring spring force is:
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A block of mass \( m = 10\text{ kg} \) rests on a rough horizontal floor with static friction coefficient \( \mu_s = \frac{1}{\sqrt{3}} \). A pulling force \( F \) is applied at an angle \( \theta \) above the horizontal. Calculate the minimum force magnitude \( F_{\min} \) necessary to set the block in motion and the corresponding optimal pulling angle \( \theta \). (Take \( g = 10\text{ m/s}^2 \))
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A bullet moving with speed \( v \) penetrates a distance \( s \) into a fixed wooden block before coming to rest. Assuming the resistive force of the wood is constant, the penetration distance for a bullet of identical mass entering the same block with double the initial speed \( 2v \) will be:
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A mass of \( 6\text{ kg} \) is suspended in equilibrium by a light rope of length \( 2\text{ m} \) hanging from a ceiling. A horizontal force of \( 50\text{ N} \) is applied at the midpoint P of the rope as shown in the figure. Taking \( g = 10\text{ m/s}^2 \), what is the tension in the upper segment of the rope?
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A horizontal force \( F \) is applied to a block of mass \( 2\text{ kg} \) resting on a horizontal floor with static friction coefficient \( \mu_s = 0.5 \). What is the minimum force \( F \) needed to just start moving the block? (Take \( g = 9.8\text{ m s}^{-2} \))
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A bomb shell of mass \( 15\text{ kg} \) moving along the positive x-axis at a speed of \( 12\text{ m/s} \) suddenly explodes into two fragments of masses \( 5\text{ kg} \) and \( 10\text{ kg} \). If the \( 5\text{ kg} \) fragment flies off along the positive y-axis with a speed of \( 48\text{ m/s} \), calculate the magnitude of the velocity vector of the \( 10\text{ kg} \) fragment immediately after the explosion.
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A stone of mass \( m \) is pulled downwards towards the Earth due to gravity. The force exerted by the stone on the Earth is equal to:
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A block of mass \( 2\text{ kg} \) rests on an inclined plane making an angle of \( 30^\circ \) with the horizontal. The coefficient of static friction between the block and the incline is \( \mu_s = 0.6 \). Taking \( g = 10\text{ m/s}^2 \), the magnitude of the frictional force acting on the block is:
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A constant force \( F \) applied individually to a mass \( m_1 \) produces an acceleration of \( 12\text{ m/s}^2 \), and applied to mass \( m_2 \) produces an acceleration of \( 6\text{ m/s}^2 \). If both masses are tied tightly together and pulled by the same force \( F \), the resulting acceleration will be:
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A rocket has an initial mass \( m_0 = 1000\text{ kg} \). It burns fuel and ejects exhaust gas at a constant relative velocity \( u = 500\text{ m/s} \) at a rate of \( 10\text{ kg/s} \). Neglecting gravitational effects, the instantaneous acceleration of the rocket at time \( t = 50\text{ s} \) after launch is:
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Refer to the given figure showing a car of mass \( m \) navigating a circular track of radius \( R \) banked at an angle \( \theta \). Under the maximum speed condition where static friction \( f \) acts down the incline, which pair of equilibrium equations correctly describes the force components along the vertical direction and horizontal centripetal direction?
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Match List-I with List-II: List-I List-II A Angle of repose \( \theta \) I \( g(\sin\theta - \mu_k \cos\theta) \) B Acceleration down a smooth inclined plane II \( \mu_s g \) C Acceleration down a rough inclined plane (\( \tan\theta > \mu_k \)) III \( \tan^{-1}(\mu_s) \) D Maximum acceleration of a train without block slipping on floor IV \( g \sin\theta \) Choose the correct answer from the options given below:
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Two masses \( m_1 = 3\text{ kg} \) and \( m_2 = 5\text{ kg} \) are suspended vertically from the ends of a light inextensible string passing over a smooth, mass-less pulley. If the system is released from rest, determine the tension \( T \) in the string and the acceleration \( a \) of the system. (Take \( g = 10\text{ m/s}^2 \))
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Given below are two statements: Statement I: A frame of reference moving with uniform acceleration relative to an inertial frame is a non-inertial frame of reference. Statement II: Pseudo forces must be applied to bodies when analyzing motion from within a non-inertial frame of reference to apply Newton's second law. In the light of the above statements, choose the most appropriate answer from the options given below:
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The position \( y \) of a particle of mass \( 2 \text{ kg} \) moving vertically under gravity and another vertical force is given by \( y = (5t + 3t^2) \text{ m} \). The net force acting on the particle is:
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Match List-I (Concepts in Ancient Indian Science) with List-II (Modern Physical Meaning): List-I List-II A Abhighat (अभिघात) I Continuous pressure causing motion B Tatkaliki gati (तत्कालिकी गति) II Impact force C Sanskara (संस्कार) III Instantaneous motion D Nodan (नोदन) IV Persistent tendency / Inertia Choose the correct answer from the options given below:
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A block of mass \( m = 2\text{ kg} \) is projected up a rough inclined plane of angle \( \theta = 30^\circ \) with an initial speed of \( u = 10\text{ m/s} \). The coefficient of kinetic friction between the block and the incline is \( \mu_k = \frac{1}{2\sqrt{3}} \). Taking \( g = 10\text{ m/s}^2 \), find the distance \( s \) traveled by the block up the incline before coming to instantaneous rest.
Read answer →Physics · LAWS OF MOTION
