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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.
Consider the following question and statements and decide which of the statements is sufficient to answer the question. There are seven balls of different size and colors: green yellow, blue, orange, red, pink and black. What is the order of the balls from largest to smallest? Statements: 1. The red ball is larger than the green ball. 2. The pink ball is the smallest. 3. The blue ball is the largest. 4. The green ball is larger than the yellow ball. 5. The yellow ball is larger than the orange and black balls.
Consider the following question and statements and decide which of the statements is sufficient to answer the question. There are seven balls of different size and colors: green, yellow, blue, orange, red, pink and black. What is the order of the balls from largest to smallest? Statements: 1. The red ball is larger than the green ball. 2. The pink ball is the smallest. 3. The blue ball is the largest. 4. The green ball is larger than the yellow ball. 5. The yellow ball is larger than the orange and black balls. 
Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. A man has two balls. The ratio of radius of first ball to that of the second ball is 7 : 3. Quantity I: If man cut the first ball from middle and difference between total surface area of part of first ball and total surface area of second ball is 1538.46cm2, then find the radius of smaller ball. Quantity II: If the sum of radius of two balls is 30, then what is the radius of first ball?
The figure shows a 5 cm diameter rod, 90 cm long, which is having its lower face grinded smooth. The remainder of the rod is exposed to 32 degree Celsius room air and a surface coefficient heat transfer equal to 6.8 W/m2 degree exists between the rod surface and the room air. The grinder dissipates mechanical energy at the rate of 35 W. If thermal conductivity of rod material is 41.5 W/m degree, find the temperature of the rod at the point where the grinding is taking place
Piston diameter = 0.24 m, length of stroke = 0.6 m, length of connecting rod = 1.5 m, mass of reciprocating parts = 300 kg, mass of connecting rod = 250 kg; speed of rotation = 125 r.p.m; centre of gravity of connecting rod from crank pin = 0.5 m ; Kg of the connecting rod about an axis through the centre of gravity = 0.65 m Find angular acceleration of connecting rod in rad/s2.
Consider the following statements. A. A balanced diet should include all nutrients along with roughages and water. B. Getting balanced diet is not so expensive. C. Balanced diet requirement is different for different age group. D. Balanced diet depends upon the amount of physical work. Which among the following statements are correct?
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 radius of gyration of the rod about a vertical axis through the centre of gravity.
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 boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing ?