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Physics-

General

Easy

Question

Three point particles P, Q, R move in circle of radius ‘r’ with different but constant speeds. They start moving at t = 0 from their initial positions as shown in the figure. The angular velocities (in rad/ sec) of P, Q and R are 5p, 2p & 3p respectively, in the same sense. The time interval after which they are at same angular position

2/3 sec
1/6 sec
1/2 sec
3/2 sec

The correct answer is: 3/2 sec

Related Questions to study

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. The radius of curvature of its trajectory when it just leaves the track at B is:

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. The radius of curvature of its trajectory when it just leaves the track at B is:

physics-General

If $f left parenthesis x comma y right parenthesis to the power of minus end exponent square root of x to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of left parenthesis x minus 1 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of x to the power of 2 end exponent plus left parenthesis y minus 1 right parenthesis to the power of 2 end exponent end root plus square root of left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus left parenthesis y minus 4 right parenthesis to the power of 2 end exponent end root comma$ where $x comma y stack I with hat on top R comma$ then the minimum value of $f left parenthesis x comma y right parenthesis$ is

If $f left parenthesis x comma y right parenthesis to the power of minus end exponent square root of x to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of left parenthesis x minus 1 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of x to the power of 2 end exponent plus left parenthesis y minus 1 right parenthesis to the power of 2 end exponent end root plus square root of left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus left parenthesis y minus 4 right parenthesis to the power of 2 end exponent end root comma$ where $x comma y stack I with hat on top R comma$ then the minimum value of $f left parenthesis x comma y right parenthesis$ is

Let $f left parenthesis x right parenthesis equals l n invisible function application open parentheses fraction numerator 1 minus x over denominator 1 plus x end fraction close parentheses$ the set of values of ‘ a ’ for which $f left parenthesis alpha right parenthesis plus f open parentheses alpha to the power of 2 end exponent close parentheses equals f open parentheses fraction numerator alpha over denominator alpha to the power of 2 end exponent minus alpha plus 1 end fraction close parentheses$ is satisfied are

Let $f left parenthesis x right parenthesis equals l n invisible function application open parentheses fraction numerator 1 minus x over denominator 1 plus x end fraction close parentheses$ the set of values of ‘ a ’ for which $f left parenthesis alpha right parenthesis plus f open parentheses alpha to the power of 2 end exponent close parentheses equals f open parentheses fraction numerator alpha over denominator alpha to the power of 2 end exponent minus alpha plus 1 end fraction close parentheses$ is satisfied are

parallel

If $f open parentheses x plus y close parentheses equals f open parentheses x. y close parentheses for all x comma y element of R text end text$ and f(2011)=2010 $text end text$ then f(2012)=

If $f open parentheses x plus y close parentheses equals f open parentheses x. y close parentheses for all x comma y element of R text end text$ and f(2011)=2010 $text end text$ then f(2012)=

If $2 f left parenthesis x right parenthesis plus x f open parentheses fraction numerator 1 over denominator x end fraction close parentheses minus 2 f open parentheses open vertical bar square root of 2 sin invisible function application pi open parentheses x plus fraction numerator 1 over denominator 4 end fraction close parentheses close vertical bar close parentheses equals 4 c o s to the power of 2 end exponent invisible function application open parentheses fraction numerator pi x over denominator 2 end fraction close parentheses plus x c o s invisible function application fraction numerator pi over denominator x end fraction comma for all x element of R minus left curly bracket 0 right curly bracket$ then which of the following statement(s) is/are true?

If $2 f left parenthesis x right parenthesis plus x f open parentheses fraction numerator 1 over denominator x end fraction close parentheses minus 2 f open parentheses open vertical bar square root of 2 sin invisible function application pi open parentheses x plus fraction numerator 1 over denominator 4 end fraction close parentheses close vertical bar close parentheses equals 4 c o s to the power of 2 end exponent invisible function application open parentheses fraction numerator pi x over denominator 2 end fraction close parentheses plus x c o s invisible function application fraction numerator pi over denominator x end fraction comma for all x element of R minus left curly bracket 0 right curly bracket$ then which of the following statement(s) is/are true?

Period of $f left parenthesis x right parenthesis equals s i n invisible function application fraction numerator pi x over denominator left parenthesis n minus 1 right parenthesis factorial end fraction plus c o s invisible function application fraction numerator pi x over denominator n factorial end fraction$ Is

Period of $f left parenthesis x right parenthesis equals s i n invisible function application fraction numerator pi x over denominator left parenthesis n minus 1 right parenthesis factorial end fraction plus c o s invisible function application fraction numerator pi x over denominator n factorial end fraction$ Is

parallel

Consider the function $f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals x open parentheses 1 minus x to the power of 2 end exponent close parentheses$ then which of the following does not hold good?

Consider the function $f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals x open parentheses 1 minus x to the power of 2 end exponent close parentheses$ then which of the following does not hold good?

The domain of the function $square root of 1 minus f left parenthesis x right parenthesis end root text where end text f to the power of 3 end exponent left parenthesis x right parenthesis equals 1 minus x to the power of 3 end exponent minus 3 x f left parenthesis x right parenthesis. x element of R text is end text left parenthesis f left parenthesis 1 right parenthesis not equal to negative 1 right parenthesis$

The domain of the function $square root of 1 minus f left parenthesis x right parenthesis end root text where end text f to the power of 3 end exponent left parenthesis x right parenthesis equals 1 minus x to the power of 3 end exponent minus 3 x f left parenthesis x right parenthesis. x element of R text is end text left parenthesis f left parenthesis 1 right parenthesis not equal to negative 1 right parenthesis$

If $f left parenthesis x right parenthesis equals s i n to the power of negative 1 end exponent invisible function application x text and end text g left parenthesis x right parenthesis equals left square bracket s i n invisible function application x left parenthesis c o s invisible function application x right parenthesis right square bracket plus left square bracket c o s invisible function application left parenthesis s i n invisible function application x right parenthesis right square bracket comma text end text$ then range of f(g(x)) is

If $f left parenthesis x right parenthesis equals s i n to the power of negative 1 end exponent invisible function application x text and end text g left parenthesis x right parenthesis equals left square bracket s i n invisible function application x left parenthesis c o s invisible function application x right parenthesis right square bracket plus left square bracket c o s invisible function application left parenthesis s i n invisible function application x right parenthesis right square bracket comma text end text$ then range of f(g(x)) is

parallel

Domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of l n invisible function application c o t to the power of negative 1 end exponent invisible function application x end root end fraction$ is

Domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of l n invisible function application c o t to the power of negative 1 end exponent invisible function application x end root end fraction$ is

If $f colon left parenthesis 0 comma pi right parenthesis rightwards arrow R$ defined by $f open parentheses x close parentheses equals stretchy sum from k equals 1 to n of open square brackets 1 plus sin invisible function application k x close square brackets comma$ where [x] denotes the integral part of x, then range of f(x) is

If $f colon left parenthesis 0 comma pi right parenthesis rightwards arrow R$ defined by $f open parentheses x close parentheses equals stretchy sum from k equals 1 to n of open square brackets 1 plus sin invisible function application k x close square brackets comma$ where [x] denotes the integral part of x, then range of f(x) is

If [x] denotes the integral part of x, then domain of the function $f left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction plus s i n to the power of negative 1 end exponent invisible function application open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets$ is

If [x] denotes the integral part of x, then domain of the function $f left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction plus s i n to the power of negative 1 end exponent invisible function application open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets$ is

parallel

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction$ is

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction$ is

The domain of definition of the function $Error converting from MathML to accessible text.$

The domain of definition of the function $Error converting from MathML to accessible text.$

Let $f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R$ be a function defined as $y equals f left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket$ ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

Let $f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R$ be a function defined as $y equals f left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket$ ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

parallel

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