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Q1. A particle moves in a circular orbit in an attractive potential V(r). Expand Lagrangian to second order about equilibrium coordinates, r_0, phi = wt and find the condition for stability against small oscillations.
Q2. What is the force of gravity between two 1490 kg cars separated by the distance of 33 m on an interstate highway?
Light of wavelength 540 nm is diffracted by a grating ruled with 1000 lines/cm. There are a total of 2000 lines in the grating. Find the angular deviation of the third order image.
Calculate P necessary to just start opening the 2 m wide gate.
A submarine dives 90.0 m at an angle of 8.0° below the horizontal. What are the horizontal and vertical components of submarine's displacement? (Imagine that upward and the direction of the submarine's horizontal motion is positive.)
Describe the full annealing heat treatment for a plain carbon steel.
A block of weight W can slide on a horizontal surface. A force of W/n1 is applied to the right that causes the block to accelerate with acceleration equal to g/n2. g is the acceleration by reason of gravity. If the coefficient of kinetic friction is ..
Find out the lengths of acceleration and deceleration phases
Two blocks are connected by a string. The smooth inclined surface makes an angle of 35 degrees with the horizontal, and the block on the incline has a mass of 5.70 kg. The mass of the hanging block is m= 2.90 kg. Find the direction of the hanging blo..
An automobile club plans to race a 780 kg car at the local racetrack. The car needs to be able to travel around several 170 m radius curves at 85 km/h. What must the banking angle of the curves be so that the force of the pavement on the tires of the..
Find the typical speed for a tsunami. (Note down that in the open ocean, tsunamis generally have amplitude of less than a meter, allowing them to pass ships unnoticed. As they approach shore, however, water depth decreases and the waves slow down. Th..
Find the gage pressure at the center of pipe A in pounds per square inch and in kilopascals.
Identical samples containing 32P are measured for a period of 1 hr in a counter having an efficiency of 44 percent and a negligible background. From a large number of observations, the mean number of counts in 1 hr is (2.93 x 10^4)
The cockroach finds a bread crumb on the rim and, of course, stops. What is an angular speed of the lazy Susan after the cockroach stops.
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