Physics-
General
Easy
Question
A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that
is equal to
Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is![](data:image/png;base64,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)
The correct answer is: ![fraction numerator L over denominator 5 end fraction](data:image/png;base64,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)
According to question,
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/899107/1/982533/Picture2.png)
![fraction numerator 1 over denominator 2 l end fraction square root of fraction numerator T subscript 1 end subscript over denominator mu end fraction end root equals fraction numerator 1 over denominator l end fraction square root of fraction numerator T subscript 2 end subscript over denominator mu end fraction end root](data:image/png;base64,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)
![T subscript 2 end subscript equals T subscript 1 end subscript divided by 4](data:image/png;base64,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)
For rotational equilibrium,
![T subscript 1 end subscript x equals T subscript 2 end subscript open parentheses L minus x close parentheses rightwards double arrow x minus L divided by 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAATCAYAAAAptGm4AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAxlJREFUeNrtWsFLlEEU/1hkiRAvIiHdRMSDSBARsoQXkYgIETqEJwkiRCIi8CARIcLiwYN0C+kgIkR4kJAgQkQWLxLRKYKI/gEPERHLwvYbeNImM/PNm5lvnN3mBz9wnd3ZN783b+a9t1+WJcgwB1Yjtq9KNib8i0tgLcngjlHwsA3srJGtCX/xApyx/XAJrINNDev0vtjg2/YanSgy/IpIg8vgQQdvaK7WfeA3yWd0+0KLIfBjm4rnYrvuOh0EP0W21gMKhk6DjdaL4BPJ/5u2RkyDm20qoIvtK+C8YmwK3IpsrQ8ir11swdW6RLdAn88geAY+dljEXYVzlmisSLjY/ha8phh7Ci4E2AAc7cbA9xbfIfTpidiXXK3vgOuKMesgeA3eclzIB/BCy+tZ8Lnm/U0DFm37D7CsGHtFJ1QImGpXJpu5EKnDd7BSkC9dwdValxZaB8FXsN9xIdfBVfp7wvLECm17QzP2BbwYaA0c7eoOh4rgskEBGtqXHK3z2qInjRFxWOyCj8DuvEm7wJ+eFvMOHKdCtTfA5nG1vaHJOTnz+rjVTLWrO6x3nWzZ9OxLl/VztTZti3bRbSGK58/gsO7NIs/c87QpH5KTRgNtHFfbVenQVY+a+NROlw6Z3gTVzKwVyfGlCzhaq9qieZgE9/OKjJc5kwxRROlakRXKz1dpzhDIs731dwNxhQ5KTruKpSY+YaqdbWHMrQlC+pKjtaotaoLfusE1g6p/A7ynOZ0HwB3wPOVfR4HSIRPbT67cOSr4WqFqka5RMRgCHO3myWab7lB3Afb48uGsoQ9VbdE8jFDtqMQ2eIOR+8quqN1TQt2kwCkaHNtlp4GqyNqm4rBocLUr+seys/Clqda6tujp+cYoaEo0twiAad2HjsFzlkFQpi+VVfZbATYSx/ZxRV54KMl7jzU5ddmT7Vztin5s4qx8aaq16QFwm7pNDZpbtF+v+DS4mbUn+unEH5CMpQfoEjo+CERR/ybT/5ZwP4v7cYQVqskSUhBY3QAix+1Jrkv4X4NABMBwcluCr81v81xPsjshOvwBQlweUhk9dDkAAAEldEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPlQ8L21pPjxtbj4xPC9tbj48L21zdWI+PG1pPng8L21pPjxtbz49PC9tbz48bXN1Yj48bWk+VDwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWk+TDwvbWk+PG1vPi08L21vPjxtaT54PC9taT48L21yb3c+PC9tZmVuY2VkPjxtbz4mI3gyMUQyOzwvbW8+PG1pPng8L21pPjxtbz4tPC9tbz48bWk+TDwvbWk+PG1vPi88L21vPjxtbj41PC9tbj48L21hdGg+pfVtZQAAAABJRU5ErkJggg==)
Related Questions to study
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Maths-General
Maths-
If
x sin x dx = – x cos x +
, then
=
If
x sin x dx = – x cos x +
, then
=
Maths-General
maths-
The equation of the tangent to the parabola y = (x – 3)2 parallel to the chord joining the points (3, 0) and (4, 1) is -
The equation of the tangent to the parabola y = (x – 3)2 parallel to the chord joining the points (3, 0) and (4, 1) is -
maths-General
maths-
The line x + y = a touches the parabola y = x – x2, and f (x) = sin2 x + sin2
+ cosx cos
, g
= 1, b = (gof) (x), then
The line x + y = a touches the parabola y = x – x2, and f (x) = sin2 x + sin2
+ cosx cos
, g
= 1, b = (gof) (x), then
maths-General
maths-
If θ be the angle subtended at the focus by the normal chord at the point (λ,λ ),λ ≠ 0 on the parabola y2 = 4ax, then equation of the line through (1, 2) and making and angle θ with x-axis is
If θ be the angle subtended at the focus by the normal chord at the point (λ,λ ),λ ≠ 0 on the parabola y2 = 4ax, then equation of the line through (1, 2) and making and angle θ with x-axis is
maths-General
maths-
The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then
The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then
maths-General
maths-
The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is
The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is
maths-General
maths-
A line L passing through the focus of the parabola y2 = 4(x –1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then
A line L passing through the focus of the parabola y2 = 4(x –1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then
maths-General
maths-
The triangle formed by tangent to the parabola y = x2 at the point whose abscissa is x0 (where x0
[1, 2]), the y-axis and the straight line y = x02 has the greatest area if x0 is equal to-
The triangle formed by tangent to the parabola y = x2 at the point whose abscissa is x0 (where x0
[1, 2]), the y-axis and the straight line y = x02 has the greatest area if x0 is equal to-
maths-General
maths-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
maths-General
maths-
If f (x) =
and
be the values of x, where f (f(x)) is not defined, then a ray of light parallel to the axis of the parabola y2 = 4x after reflection from the internal surface of the parabola will necessarily pass through the point.
If f (x) =
and
be the values of x, where f (f(x)) is not defined, then a ray of light parallel to the axis of the parabola y2 = 4x after reflection from the internal surface of the parabola will necessarily pass through the point.
maths-General
maths-
If the normal at three points (ap2, 2ap), (aq2, 2aq) and (ar2, 2ar) are concurrent then the common root of equations px2 + qx + r = 0 and a(b – c) x2 + b (c – a) x + c(a – b) = 0 is
If the normal at three points (ap2, 2ap), (aq2, 2aq) and (ar2, 2ar) are concurrent then the common root of equations px2 + qx + r = 0 and a(b – c) x2 + b (c – a) x + c(a – b) = 0 is
maths-General
physics-
A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
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)
A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle
to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle
=
will be
![](data:image/png;base64,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)
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle
to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle
=
will be
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)
physics-General