Question
Explain the international system of units. Explain its characteristics.
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Answer
self
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Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar. Consider a plane making an angle $\Delta$ with the length. What are the tensile and shearing stresses on this plane?
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- For what angle is the tensile stress a maximum?
- For what angle is the shearing stress a maximum?
The periodic time of a mass suspended by a spring (force constant K) is T. If the spring is cut in three equal pieces, what will be the force constant of each part? If the same mass be suspended from one piece, what will be the periodic time?
Consider the situation of the previous problem. Suppose each of the blocks is pulled by a constant force F instead of any impulse. Find the maximum elongation that the spring will suffer and the distances moved by the two blocks in the process.
Give the description of Carnot cycle and calculate the total work done in one cycle and establish the formula for the efficiency of Carnot engine. Also write Carnot theorem.
Two cars, A and B are travelling in the same direction with the velocities va and vb respectively. When the car A is at a distance d, and behind the car B, the brakes are applied on A, causing a deceleration at the rate 'a'. Show that to prevent a collision between A and B, it is necessary that $\text{v}_\text{a}-\text{v}_\text{b}<\sqrt{2\text{ad}}.$
→A ball is thrown vertically upwards with a velocity of $20 m s ^{-1}$ from the top of a multistorey building. The height of the point from where the ball is thrown is $25.0 m$ from the ground. (a) How high will the ball rlse? and (b) how long will it be before the ball hits the ground? Take $g =10 m s ^{-2}$.
→A spring having with a spring constant $1200 N m ^{-1}$ is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.
Take the position of mass when the spring is unstreched as $x=0$, and the direction from left to right as the positive direction of $x$-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch $(t=0)$, the mass is
a. at the mean position,
b. at the maximum stretched position, and
c. at the maximum compressed position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
→Take the position of mass when the spring is unstreched as $x=0$, and the direction from left to right as the positive direction of $x$-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch $(t=0)$, the mass is
a. at the mean position,
b. at the maximum stretched position, and
c. at the maximum compressed position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
A slightly tapering wire of length I and end radii a and b on both sides is subjected to the stretching forces F on both sides as shown in figure. If Y is the Young's modulus of the wire, calculate the extension produced in the wire.
A uniform chain of length L and mass M overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is $\mu.$ Find the work done by the friction during the period the chain slips off the table.
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