Physics-
General
Easy

Question

After the drop detaches its surface energy is

  1. 1.4 cross times 10 to the power of negative 6 end exponent straight J
  2. 2.6 cross times 10 to the power of negative 6 end exponent straight J
  3. 5.4 cross times 10 to the power of negative 6 end exponent straight J
  4. 8.1 cross times 10 to the power of negative 6 end exponent straight J

The correct answer is: 2.6 cross times 10 to the power of negative 6 end exponent straight J

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If ell equals 5 cross times 10 to the power of negative 4 end exponent straight m comma rho equals 10 cubed kgm to the power of negative 3 end exponent equals 10 ms to the power of negative 2 end exponent straight T equals 0.11 Nm to the power of negative 1 end exponent the......... radius of the drop when it detaches from the dropper is approximately

If ell equals 5 cross times 10 to the power of negative 4 end exponent straight m comma rho equals 10 cubed kgm to the power of negative 3 end exponent equals 10 ms to the power of negative 2 end exponent straight T equals 0.11 Nm to the power of negative 1 end exponent the......... radius of the drop when it detaches from the dropper is approximately

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text  If  end text f left parenthesis 9 right parenthesis equals 9 comma f to the power of apostrophe left parenthesis 9 right parenthesis equals 4 comma text  then  end text space text  Lt end text subscript x not stretchy rightwards arrow 9 end subscript fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction text  equals  end text

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text  If  end text f left parenthesis 9 right parenthesis equals 9 comma f to the power of apostrophe left parenthesis 9 right parenthesis equals 4 comma text  then  end text space text  Lt end text subscript x not stretchy rightwards arrow 9 end subscript fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction text  equals  end text

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If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r<<R) is:

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L t subscript x not stretchy rightwards arrow negative straight infinity end subscript open square brackets fraction numerator x to the power of 4 sin space open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets equals

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Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x where a,b,c are real and non-zero=

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The basic problem of this indeterminate form is to know from where f not stretchy left parenthesis x not stretchy right parenthesis tends to one (right or left) and what function reaches its limit more rapidly.

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Which graph present the variation of surface tension with temperature over small temperature ranges for coater.

Which graph present the variation of surface tension with temperature over small temperature ranges for coater.

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Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 1 end exponent

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The basic problem of this indeterminate form is to know from where f not stretchy left parenthesis x not stretchy right parenthesis tends to one (right or left) and what function reaches its limit more rapidly.

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text  Lt  end text subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 2 end exponent equals

The basic problem of this indeterminate form is to know from where f not stretchy left parenthesis x not stretchy right parenthesis tends to one (right or left) and what function reaches its limit more rapidly.

text  Lt  end text subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 2 end exponent equals

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The basic problem of this indeterminate form is to know from where f not stretchy left parenthesis x not stretchy right parenthesis tends to one (right or left) and what function reaches its limit more rapidly.

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Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals

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Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals

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L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals

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text  If  end text a greater than 0 text  and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of a minus x to the power of a over denominator x to the power of a minus a to the power of a end fraction equals negative 1 text , then  end text bold a equals

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text  If  end text a greater than 0 text  and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of a minus x to the power of a over denominator x to the power of a minus a to the power of a end fraction equals negative 1 text , then  end text bold a equals

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We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or  fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

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We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos space x right parenthesis minus b sin space x over denominator x cubed end fraction equals 1 text  then  end text straight a equals comma straight b equals

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We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

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