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If the earth suddenly shrinks to (1/27)th of its original volume with no change in mass, what is the new duration of a day ?
9/10 volume of an ice cube is floating down the surface of sea water.find the density of the ice cube
A speaker, playing a sound at some unknown frequency, is placed near the opening of a tube partially filled with water (the water acts as a fixed boundary). You come into the room and notice that water level in the tube is already dropping. You hear a loud sound (harmonic frequency) and you note the water level is L_A = 1.10 m. You keep listening as the water level falls until you here the next loud sound but you miss the water level. You continue to listen until you hear the next loud sound at L_C = 1.980 m. (If you require the speed of the sound in air, you can take it to be 343 m/s).

A) Sketch any three consecutive harmonics associated with a tube as described above. Label both ends as either fixed or free and label all Nodes and Antinodes.
B) Derive the formula for the harmonic frequencies of this type of tube. State what the allowed values for n are.
C) Find the frequency the speaker is emitting?
Consider a hill with a slope of 30 degrees relative to the horizontal direction. I push a ball of mass 2 kg directly up the slope, and as I do so, I take ten steps, walking up the slope, with each step being 50 cm long. Presuming that the downward (i.e., vertical) force, in newtons, exerted by gravity on the ball is 9.8 times the mass of the ball in kg, by how many joules has the potential energy of the ball increased?
2 equal uniform rods AB and BC each of weight W are smoothly jointed using a light inextensible string at the vertices A and C which makes a right angle at ABC. The system is freely hinged at vertex a to a fixed point and hanging in a vertical plane. If the system is in equilibrium show that the tension in the string is 3W/2(root 5)
Four uniform smooth rods each of length to 2b and weight W are smoothly jointed had A,B,C and D to form a rhombus ABCD the system is kept in equilibrium in a vertical plane so that the rods AB and AD rest upon 2 pegs at the same horizontal level. The distance between the pegs is to 2a. The rods AB and AD each makes an angle theta to the vertical. A weight of W hangs at the lowest point C. Show that the reaction on the peg is (5Wcosec theta)/2
To win the game, a place kicker must kick a
football from a point 19 m (20.7784 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 15 m/s at
an angle of 51.7

from the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
By how much vertical distance does the ball
clear the crossbar?
by what method can you distinguish between a converging lens and diverging lens?
A car moves 30km/hr for 10 minutes and 50km/hr for 20 minutes. What is its average speed?
A train is on its way to deliver its cargo. The train is travelling at 90 km/h along a straight section of track. It has to cross a bridge to reach the destination. A girl is on the bridge, 2/5 of the way from the train side. The girl can just barely escape the oncoming train by running in either direction. How fast, in km/h, can the girl run? (Assume no acceleration of the girl, instantly at her constant speed.)
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