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Physics-

General

Easy

Question

In the figure shown a hole of radius 2 cm is made in a semicircular disc of radius 6 $pi$ at a distance 8 cm from the centre C of the disc. The distance of the centre of mass of this system from point C is :

4 cm
8 cm
6 cm
12 cm

The correct answer is: 8 cm

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From a uniform disc of radius R, an equilateral triangle of side $square root of 3 R$ is cut as shown. The new position of centre of mass is :

From a uniform disc of radius R, an equilateral triangle of side $square root of 3 R$ is cut as shown. The new position of centre of mass is :

Physics-General

The dumbell is placed on a frictionless horizontal table. Sphere A is attached to a frictionless pivot so that B can be made to rotate about A with constant angular velocity. If B makes one revolution in period P, the tension in the rod is

The dumbell is placed on a frictionless horizontal table. Sphere A is attached to a frictionless pivot so that B can be made to rotate about A with constant angular velocity. If B makes one revolution in period P, the tension in the rod is

Physics-General

A hollow vertical cylinder of radius R is rotated with angular velocity w about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass M suspended on the inside of the cylinder as it rotates?

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Physics-General

parallel

$I f tan space alpha comma tan space beta$ are the roots of the equation $x squared plus p x plus q equals 0 left parenthesis p not equal to 0 right parenthesis$ then $s i n squared invisible function application left parenthesis alpha plus beta right parenthesis plus p s i n invisible function application left parenthesis alpha plus beta right parenthesis c o s invisible function application left parenthesis alpha plus beta right parenthesis plus q c o s squared invisible function application left parenthesis alpha plus beta right parenthesis equals$

$I f tan space alpha comma tan space beta$ are the roots of the equation $x squared plus p x plus q equals 0 left parenthesis p not equal to 0 right parenthesis$ then $s i n squared invisible function application left parenthesis alpha plus beta right parenthesis plus p s i n invisible function application left parenthesis alpha plus beta right parenthesis c o s invisible function application left parenthesis alpha plus beta right parenthesis plus q c o s squared invisible function application left parenthesis alpha plus beta right parenthesis equals$

$cos space left parenthesis x minus y right parenthesis plus cos space left parenthesis y minus z right parenthesis plus cos space left parenthesis z minus x right parenthesis equals negative 3 over 2 not stretchy rightwards double arrow sum left parenthesis cos space x right parenthesis equals$

$cos space left parenthesis x minus y right parenthesis plus cos space left parenthesis y minus z right parenthesis plus cos space left parenthesis z minus x right parenthesis equals negative 3 over 2 not stretchy rightwards double arrow sum left parenthesis cos space x right parenthesis equals$

$text In a end text straight triangle A B C comma text if end text sin text end text A sin space B sin space C equals 1 third$ then the value of $c o t space A c o t space B plus c o t space B c o t space C plus c o t space C c o t space A$ is

$text In a end text straight triangle A B C comma text if end text sin text end text A sin space B sin space C equals 1 third$ then the value of $c o t space A c o t space B plus c o t space B c o t space C plus c o t space C c o t space A$ is

parallel

$cot invisible function application A plus cot invisible function application B plus cot invisible function application C plus fraction numerator cos invisible function application left parenthesis A plus B plus C right parenthesis over denominator sin invisible function application A sin invisible function application B sin invisible function application C end fraction equals$

$cot invisible function application A plus cot invisible function application B plus cot invisible function application C plus fraction numerator cos invisible function application left parenthesis A plus B plus C right parenthesis over denominator sin invisible function application A sin invisible function application B sin invisible function application C end fraction equals$

$text In a end text straight triangle A B C comma tan invisible function application A plus tan invisible function application B plus tan invisible function application C equals 6$ and $tan invisible function application A tan invisible function application B equals 2$ then the triangle $A B C$ is

$text In a end text straight triangle A B C comma tan invisible function application A plus tan invisible function application B plus tan invisible function application C equals 6$ and $tan invisible function application A tan invisible function application B equals 2$ then the triangle $A B C$ is

$text If end text tan invisible function application straight A equals 1 comma tan invisible function application straight B equals 2 comma tan invisible function application straight C equals 3 text then end text straight A plus straight B plus straight C equals$

$text If end text tan invisible function application straight A equals 1 comma tan invisible function application straight B equals 2 comma tan invisible function application straight C equals 3 text then end text straight A plus straight B plus straight C equals$

parallel

$text If end text alpha plus beta plus gamma equals pi over 2 text and end text cot invisible function application alpha comma cot invisible function application beta comma cot invisible function application gamma text are in end text straight A stack P with _ below with _ below text then end text cot invisible function application alpha times cot invisible function application gamma equals$

$text If end text alpha plus beta plus gamma equals pi over 2 text and end text cot invisible function application alpha comma cot invisible function application beta comma cot invisible function application gamma text are in end text straight A stack P with _ below with _ below text then end text cot invisible function application alpha times cot invisible function application gamma equals$

if $tan space alpha comma tan space beta$ are the roots of the equation, $x squared plus p x plus q equals 0 left parenthesis p not equal to 0 right parenthesis$ then

if $tan space alpha comma tan space beta$ are the roots of the equation, $x squared plus p x plus q equals 0 left parenthesis p not equal to 0 right parenthesis$ then

$cot space B equals 2 tan space left parenthesis A minus B right parenthesis not stretchy rightwards double arrow 2 tan space B plus cot space B equals$

$cot space B equals 2 tan space left parenthesis A minus B right parenthesis not stretchy rightwards double arrow 2 tan space B plus cot space B equals$

parallel

$text If end text sin text end text B equals 1 fifth times sin space left parenthesis 2 A plus B right parenthesis text then end text fraction numerator tan begin display style text end text end style left parenthesis A plus B right parenthesis over denominator tan begin display style text end text end style A end fraction equals$

$text If end text sin text end text B equals 1 fifth times sin space left parenthesis 2 A plus B right parenthesis text then end text fraction numerator tan begin display style text end text end style left parenthesis A plus B right parenthesis over denominator tan begin display style text end text end style A end fraction equals$

$text If end text sin text end text x plus sin space y equals 3 left parenthesis cos space y minus cos space x right parenthesis text then end text fraction numerator sin begin display style text end text end style 3 x over denominator sin begin display style text end text end style 3 y end fraction equals$

$text If end text sin text end text x plus sin space y equals 3 left parenthesis cos space y minus cos space x right parenthesis text then end text fraction numerator sin begin display style text end text end style 3 x over denominator sin begin display style text end text end style 3 y end fraction equals$

$cos squared space left parenthesis A minus B right parenthesis plus cos squared space B minus 2 cos space left parenthesis A minus B right parenthesis cos A cos space B equals$

$cos squared space left parenthesis A minus B right parenthesis plus cos squared space B minus 2 cos space left parenthesis A minus B right parenthesis cos A cos space B equals$

parallel

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