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A uniform disc of mass M and radius R is supported vertically by a pivot at its periphery as shown. A particle of mass M is fixed to the rim and raised to the highest point above the centre. The system is then released from rest and it can rotate about its pivot freely. The angular speed of the system when the attached object is directly beneath the pivot is
The correct answer is:
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Two trolleys 1 and 2 are moving with accelerations a1 and a2 respectively in the same direction. A block of mass ‘’m’’ on trolley 1 is in equilibrium from the frame of observer stationary w.r.t. trolley 2. The magnitude of friction force on block due to trolley is (assume that no horizontal force other than friction force is acting on block) 
Two trolleys 1 and 2 are moving with accelerations a1 and a2 respectively in the same direction. A block of mass ‘’m’’ on trolley 1 is in equilibrium from the frame of observer stationary w.r.t. trolley 2. The magnitude of friction force on block due to trolley is (assume that no horizontal force other than friction force is acting on block)
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Acceleration versus time curve for a particle moving in a straight line is shown in the figure. If particle starts from rest at t = 0, then which of the following curve is true for the same particle
Acceleration versus time curve for a particle moving in a straight line is shown in the figure. If particle starts from rest at t = 0, then which of the following curve is true for the same particle
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In the figure shown a ring A is initially rolling without sliding with a velocity v on the horizontal surface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity. What will be the maximum height reached by A on B.
In the figure shown a ring A is initially rolling without sliding with a velocity v on the horizontal surface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity. What will be the maximum height reached by A on B.
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A small block of mass m is placed on a wedge of mass M as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant k. If a' is the acceleration of m relative to the wedge as it starts coming down and A is the acceleration acquired by the wedge as the block starts coming down, then
A small block of mass m is placed on a wedge of mass M as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant k. If a' is the acceleration of m relative to the wedge as it starts coming down and A is the acceleration acquired by the wedge as the block starts coming down, then
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A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
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One ice skater of mass m moves with speed 2v to the right, while another of the same mass m moves with speed v toward the left, as shown in figure I. Their paths are separated by a distance b. At t = 0, when they are both at x = 0, they grasp a pole of length b and negligible mass. For t > 0, consider the system as a rigid body of two masses m separated by distance b, as shown in figure II. Which of the following is the correct formula for the motion after t = 0 of the skater initially at y = b/2?
One ice skater of mass m moves with speed 2v to the right, while another of the same mass m moves with speed v toward the left, as shown in figure I. Their paths are separated by a distance b. At t = 0, when they are both at x = 0, they grasp a pole of length b and negligible mass. For t > 0, consider the system as a rigid body of two masses m separated by distance b, as shown in figure II. Which of the following is the correct formula for the motion after t = 0 of the skater initially at y = b/2?
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Two light vertical springs with equal natural lengths and spring constants k1 and k2 are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is
Two light vertical springs with equal natural lengths and spring constants k1 and k2 are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is
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A conical pendulum consists of a mass M suspended from a string of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t, the mass is at position i 
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. At time t, the angular momentum vector of the mass M about the point from which the string suspended is :
A conical pendulum consists of a mass M suspended from a string of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t, the mass is at position i and has velocity . At time t, the angular momentum vector of the mass M about the point from which the string suspended is :
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In the previous problem, the steel rope is vertical and moving with the force acting vertically up at the upper end. The strain at a point L/3 from lower end is
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In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
In the above question the rate of increase of the kinetic energy of the cart (with sand) is v
In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
In the above question the rate of increase of the kinetic energy of the cart (with sand) is v
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In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
In the same model of the above question if the cart is to be moved with constant velocity v, then the power supplied by external agent applying that force is v v
In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
In the same model of the above question if the cart is to be moved with constant velocity v, then the power supplied by external agent applying that force is v v
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In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
The velocity of the cart at time 
In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling kg/s and sticksmfrom a stationary hopper on to the cart with negligible velocity at constant rate to the cart.
The velocity of the cart at time
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Two bodies have undergone an elastic one–dimensional collision along x–axis. Figure is a graph of position versus time for these bodies and for their center of mass.
The mass of the body that was moving faster before the collision is ________ that of other body.
Two bodies have undergone an elastic one–dimensional collision along x–axis. Figure is a graph of position versus time for these bodies and for their center of mass.
The mass of the body that was moving faster before the collision is ________ that of other body.
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Two bodies have undergone an elastic one–dimensional collision along x–axis. Figure is a graph of position versus time for these bodies and for their center of mass.
Which line segment corresponds to the motion of the center of mass before and after the collision?
Two bodies have undergone an elastic one–dimensional collision along x–axis. Figure is a graph of position versus time for these bodies and for their center of mass.
Which line segment corresponds to the motion of the center of mass before and after the collision?
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A bob of mass 10 M is suspended through an inextensible string of length l. When the bob is at rest at the equilibrium position, two particles of mass m each moving with velocity u making an angle 60° with the string strike and get simultaneously attached to the bob. What is the value of impulsive tension (l) in the string during the impact ?
A bob of mass 10 M is suspended through an inextensible string of length l. When the bob is at rest at the equilibrium position, two particles of mass m each moving with velocity u making an angle 60° with the string strike and get simultaneously attached to the bob. What is the value of impulsive tension (l) in the string during the impact ?
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