Solid Cylinder Rolling Without Slipping on Hollow Cylinder
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Questions and Answers

What is the magnitude of acceleration of point A of the solid cylinder?

  • 72ω0 R
  • 40ω0 R
  • 56ω0 R
  • 88ω0 R (correct)
  • What is the angular velocity of the solid cylinder about its own axis?

  • 8ω0
  • 6ω0
  • 10ω0 (correct)
  • 4ω0
  • In the scenario described, what is the magnitude of acceleration of point B of the solid cylinder with respect to the contact surface of the hollow cylinder?

  • 112ω0 R (correct)
  • 96ω0 R
  • 64ω0 R
  • 80ω0 R
  • What is the radius of curvature of point A at the given instant?

    <p>32R</p> Signup and view all the answers

    When a hollow tube containing a ball is accelerated horizontally and the ball is slightly displaced from point 'A', what represents the approximate nature of N1 and N2?

    <p>|N1| &gt; |N2|</p> Signup and view all the answers

    In the scenario described with the hollow tube and a ball, what relationship between N1 and N2 can be observed?

    <p>|N1| &lt; |N2|</p> Signup and view all the answers

    In which of the following cases, if plate A and C are earthed, the charge on the left surface of plate B is 4Q/3?

    <p>(II), (iii), (Q)</p> Signup and view all the answers

    If plate B is earthed, in which of the following cases does the sum of the charges on plates A and C equal 2Q?

    <p>(III), (iv), (P)</p> Signup and view all the answers

    What is the single digit integer answer to the question involving the surface mass density of a semi-circular disc with a given force applied for translational motion?

    <p>5</p> Signup and view all the answers

    If a box with attached plates AB and CD is released on an inclined plane, what is the angle of inclination of the plane?

    <p>45 degrees</p> Signup and view all the answers

    For the situation involving a semi-circular disc, what does the parameter 'h' represent?

    <p>Height</p> Signup and view all the answers

    Given the information about the force applied to the semi-circular disc, what does the constant 'k' represent?

    <p>Pi</p> Signup and view all the answers

    Which reagent from the table is capable of converting benzene into a mixture of two carboxylic acids?

    <p>Ac2O / AlCl3</p> Signup and view all the answers

    Which compound from the first column reacts with Mg / Et2O and then with CO2 to give effervescence?

    <p>Conc.HNO3</p> Signup and view all the answers

    Which reagent in the table is more acidic than water?

    <p>Conc.HNO3 / Conc.H2SO4</p> Signup and view all the answers

    Which reagent gives off H2 gas on reaction with sodium metal?

    <p>Pr opene, H3PO4</p> Signup and view all the answers

    Which compound from the first column reacts with K2Cr2O7 / Conc.H2SO4 to produce H3O+ ions?

    <p>Pr opene, H3PO4</p> Signup and view all the answers

    Which reagent from the table reacts with Br2 / NaOH and then with Fe to form CO2 and H3O+?

    <p>HeCl / AlCl3</p> Signup and view all the answers

    What is the correct integral representation for $I(\alpha)$ in Column 1?

    <p>$\int\limits_{0}^{1} \frac{x^2}{1 - x^2} \tan^{-1}(\alpha x) dx$</p> Signup and view all the answers

    If $\alpha = 1$, which combination of integrals and options in Column 2 is correct?

    <p>III, (iv), Q</p> Signup and view all the answers

    For $\alpha^2 = 4$, which set of integrals and options in Column 1 is true?

    <p>$II, (iii), R$</p> Signup and view all the answers

    Which integral expression in Column 1 corresponds to the natural logarithm of $\frac{5+1}{2}$?

    <p>$\int\limits_{0}^{1} \ln\left(\frac{17+4}{4}\right) dx$</p> Signup and view all the answers

    If $\alpha = \frac{1}{2}$, which combination of integrals and options in Column 2 is correct?

    <p>I, (ii), S</p> Signup and view all the answers

    When $\alpha^2 = 9$, which set of integrals and options in Column 1 is accurate?

    <p>$IV, (ii), S$</p> Signup and view all the answers

    What is the product of the roots of the equation $x^5 + x^2 + 1 = 0$?

    <p>-1</p> Signup and view all the answers

    What is the value of $n$ in the equation $3^{n-1} + 3^{n-2} + 3^{n-3} = a$?

    <p>$1$</p> Signup and view all the answers

    If $g(x) = x^2 - 2$, what is the value of $g(x_1) \cdot g(x_2) \cdot g(x_3) \cdot g(x_4) \cdot g(x_5) - 30g(x_1x_2x_3x_4x_5)$?

    <p>$-30$</p> Signup and view all the answers

    What is the equation of the curve obtained by reflecting the ellipse $\frac{(x-4)^2}{16} + \frac{(y-3)^2}{9} = 1$ about the line $x - y - 2 = 0$?

    <p>$16x + 9y - 36 = 0$</p> Signup and view all the answers

    In the context of vectors, if $d = \sin(x)(a \times b) + \cos(y)(b \times c) + 2(c \times b)$, what is the minimum value of $x^2 + y^2$?

    <p>$2\pi^2$</p> Signup and view all the answers

    If $a, b, c$ are non-coplanar vectors and $d = \sin(x)(a \times b) + \cos(y)(b \times c) + 2(c \times b)$, what is the sum of $a$ and $b$ when $x^2 + y^2 = \pi^2$, given that $a$ and $b$ are coprime?

    <p>$2\pi$</p> Signup and view all the answers

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