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A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time ‘t’? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.

Correct Answer: 1.25 rad/s, spheres will move to opposite ends of rod
When the rod gets an impulse, it gets an initial angular velocity. Now, the two spheres will start going outwards till they reach the end of the rod on either side as the walls of rod’s ends will provide the required centripetal force. Also, to find final angular velocity we can conserve angular momentum as there is no external torque. I1w1 = I2w2, where I1, I2, w1, w2 are the initial & final moment of inertias & angular velocities resp. I1 = MI2/12 + 0 = 2*0.01/12 = 0.01/6 kgm2. I1 = MI2/12 + 2*mI2/4 = (0.01/6) + (0.5*1*0.01) = (0.01/6) + (0.01/2) = 0.04/6 = 0.02/3 kgm2. ∴ I1w1 = I2w2 0.01/6 * 5 = 0.02/3 *w2 ∴ w2 = 1.25 rad/s.

A disc is rotating with ω =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc’s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?

What is the moment of inertia of a rod about an axis passing through the centre and perpendicular to its central axis? Given that mass of rod is 1kg, length = 10cm.

A bead of mass m slides along a straight frictionless rigid wire rotating in a horizontal plane with a constant angular speed ω. The axis of rotation is perpendicular to the wire and passes through one end of the wire. If r is the distance of the mass from the axis of rotation and v is its speed, then the magnitude of the Coriolis force is

A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the mass moment of inertia of the rod about a vertical axis through the centre of gravity.

A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult.
Why are ants called the 'Earth's' most successful species?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. Antennae are used by ants to

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What does the Western Harvester do in winter ?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What kind of homes do the army of ants build ?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What is the purpose of male ants ?