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Physics · LAWS OF MOTION
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Physics · LAWS OF MOTION
A trolley of mass \( 18\text{ kg} \) on a rough horizontal surface (\( \mu_k = 0.05 \)) is connected by a light inextensible string passing over a smooth pulley to a vertically hanging mass of \( 2\text{ kg} \). Taking \( g = 10\text{ m/s}^2 \), the common acceleration of the system is:
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A body of mass \( 10\text{ kg} \) is sliding on a horizontal plane with kinetic friction coefficient \( \mu_k = 0.2 \). If an external horizontal force of \( 30\text{ N} \) is pulled on it, the acceleration of the body is (Take \( g = 10\text{ m s}^{-2} \)):
Read answer →Physics · LAWS OF MOTION
A block of mass \( m = 2\text{ kg} \) is pressed against a rough vertical wall by applying a horizontal force \( F \). The coefficient of static friction between the block and the wall is \( \mu_s = 0.4 \). Taking \( g = 10\text{ m/s}^2 \), find the minimum horizontal force \( F_{\min} \) required to keep the block stationary. If a force \( F = 100\text{ N} \) is actually applied, calculate the magnitude of friction force acting on the block.
Read answer →Physics · LAWS OF MOTION
A small heavy bob of mass \( m \) is suspended symmetrically in equilibrium by two light strings attached to a flat horizontal ceiling. Each string makes an angle of \( 45^\circ \) with the horizontal ceiling. The tension in each string is:
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Match List-I with List-II: \n List-I List-II A Linear Momentum I Product of mass and velocity, unit \( \text{kg m s}^{-1} \) B Impulse II Product of force and time interval, unit \( \text{N s} \) C Coefficient of static friction III Ratio of limiting friction to normal reaction, unitless D Rate of change of momentum IV Equal to net external force, dimension \( [\text{M L T}^{-2}] \) \n Choose the correct answer from the options given below:
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Compared to static or sliding friction between hard surfaces, rolling friction is smaller by how many orders of magnitude?
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A time-dependent force \( \vec{F}(t) = (A t - B t^2)\hat{i} \) acts on a particle of mass \( m \) initially at rest from \( t = 0 \) to \( t = \frac{A}{B} \), where \( A \) and \( B \) are positive constants. The final velocity acquired by the particle at \( t = \frac{A}{B} \) is:
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In the given diagram showing Galileo's double inclined plane experiment, a marble is released from rest at initial height \( h \) on plane (i). In the ideal frictionless case, when plane (ii) has a smaller angle of inclination than plane (i), how does the final vertical height reached by the marble on plane (ii) compare to \( h \), and how does the distance traveled along plane (ii) compare to plane (i)?
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A block of mass \( 5\text{ kg} \) rests on a horizontal rough surface with coefficient of static friction \( \mu_s = 0.4 \). If a horizontal force of \( 15\text{ N} \) is applied on the block, the frictional force acting on the block is (Take \( g = 10\text{ m s}^{-2} \)):
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A particle of mass \( m = 2\text{ kg} \) is kept in equilibrium under the action of three concurrent forces: \( \vec{F}_1 = (2\hat{i} + 3\hat{j} - \hat{k})\text{ N} \), \( \vec{F}_2 = (-\hat{i} - 4\hat{j} + 2\hat{k})\text{ N} \), and \( \vec{F}_3 \). If the force \( \vec{F}_2 \) is suddenly removed, what will be the magnitude of the acceleration of the particle?
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Consider the following statements regarding the behavior of static friction on a block on an inclined plane: (A) Static friction is a self-adjusting force that opposes impending relative motion. (B) The magnitude of static friction cannot exceed \( \mu_s N \). (C) On an inclined plane of inclination \( \theta \), as \( \theta \) increases, the normal force increases. (D) When sliding begins, the frictional force drops slightly to kinetic friction. Which of the above statements are correct?
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An astronaut of total mass \( 80\text{ kg} \) is at rest outside a spaceship in zero-gravity space. He throws a tool of mass \( 2\text{ kg} \) directly away from himself with a velocity of \( 16\text{ m/s} \) relative to himself. The separation distance between the astronaut and the tool after \( 5\text{ s} \) is:
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A bullet of mass \( 0.04 \text{ kg} \) moving with a speed of \( 90 \text{ m s}^{-1} \) enters a heavy wooden block and is stopped after penetrating a distance of \( 60 \text{ cm} \). The average resistive force exerted by the block on the bullet is:
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A wooden block of mass \( m_1 = 3\text{ kg} \) rests on a soft horizontal floor. An iron cylinder of mass \( m_2 = 17\text{ kg} \) is placed on top of the block. The floor yields steadily, causing the block-cylinder system to accelerate downwards at \( a = 2\text{ m/s}^2 \). Taking \( g = 10\text{ m/s}^2 \), calculate (i) the normal action force exerted by the block on the floor, and (ii) the normal reaction force exerted by the cylinder on the block.
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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): Internal forces acting between different interacting particles of a system can alter the total linear momentum of the system. Reason (R): According to Newton's third law of motion, internal forces always occur in equal and opposite pairs, so their net vector sum within the system is zero. In the light of the above statements, choose the correct answer from the options given below:
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Given below are four statements regarding frictional forces and contact interactions: (A) Static friction is a self-adjusting force whose magnitude is strictly equal to \( \mu_s N \) at all times. (B) The kinetic friction force is virtually independent of the microscopic area of contact for a given pair of solid surfaces. (C) The angle of friction is equal to the angle of repose for an object on an inclined plane on the verge of sliding. (D) The magnitude of limiting static friction is directly proportional to the normal reaction force. Which of the above statements are correct?
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An astronaut of mass \( 60 \text{ kg} \) accidentally gets separated from a small spaceship accelerating at \( 100 \text{ m s}^{-2} \) in interstellar space. Assuming there are no nearby stars to exert gravitational force, the net force acting on the astronaut the instant after he is outside the spaceship is:
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A constant force \( \mathbf{F} = (6\hat{i} - 8\hat{j}) \text{ N} \) acts on a body of mass \( 5 \text{ kg} \). The magnitude of acceleration produced in the body is:
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The position of a particle of mass \( 2\text{ kg} \) moving along the x-axis is given by \( x(t) = 2 t^3 - 3 t^2 + 4 \) (where \( x \) is in meters and \( t \) in seconds). The magnitude of the impulse delivered to the particle between \( t = 1\text{ s} \) and \( t = 3\text{ s} \) is:
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A bullet of mass \( 0.05\text{ kg} \) entering a fixed wooden block with an initial horizontal speed of \( 200\text{ m/s} \) comes to rest after penetrating a distance of \( 0.5\text{ m} \). Assuming a uniform resistive retarding force, the average resistive force exerted by the block and the stopping time are respectively:
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A cricket player catches a ball of mass \( 150 \text{ g} \) moving with a speed of \( 20 \text{ m s}^{-1} \). If he brings the ball to rest in \( 0.1 \text{ s} \), the average retarding force exerted on his hands is:
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Consider the following statements regarding Newton's laws of motion: (A) The rate of change of momentum of a body is directly proportional to the applied external force and takes place in the direction of force. (B) Impulse is a scalar physical quantity equal to the product of average force and time duration. (C) Newton's second law is a vector law, which can be applied independently along three mutually perpendicular component axes. (D) Internal forces acting between particles of a system can alter the total linear momentum of the system as a whole. Which of the above statements are correct?
Read answer →Physics · LAWS OF MOTION
