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Physics-

General

Easy

Question

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg

1
2
3
4

The correct answer is: 3

Related Questions to study

A 10 kg ball attached to the end of a rigid massless rod of length 1 m rotates at constant speed in a horizontal circle of radius 0.5 m and period 1.57 sec as in fig. The force exerted by rod on the ball is

A 10 kg ball attached to the end of a rigid massless rod of length 1 m rotates at constant speed in a horizontal circle of radius 0.5 m and period 1.57 sec as in fig. The force exerted by rod on the ball is

physics-General

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

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

physics-General

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

parallel

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

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)=

parallel

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

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?

parallel

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

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

parallel

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

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

parallel

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