Centre of Mass & Momentum PYQs Set 4 (PDF)

Set 4 of 4 · Questions 91-97 of 97

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Mere Teacher · Previous Year Questions NEET Physics · Centre of Mass & Momentum · Set 4 (Q91-97)
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91. $Four identical thin rods each of mass M and length λ, form a square frame. Moment of intertia of this frame about an axis through the centre of the square and perpendicular to its plane is$ (1) $\frac{4}{3} Mλ2$ (2) $\frac{2}{3} Mλ2$ (3) $\frac{13}{3} Mλ2$ (4) $\frac{1}{3} Mλ2$ 92. $A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is αR distance from the centre of the bigger disc. The value of α is :$ (1) $1/3$ (2) $1/2$ (3) $1/6$ (4) $1/4$ 93. $A disc is rolling, the velocity of its centre of mass is v_{cm} . Which one will be correct?$ (1) $the velocity of highest point is 2 v_{cm} and point of contact is zero$ (2) $the velocity of highest point is v_{cm} and point of contact is v_{cm}$ (3) $the velocity of highest point is 2 v_{cm} and point of contact is v_{cm}$ (4) $the velocity of highest point is 2 v_{cm} and point of contact is 2 v_{cm} .$ 94. $As shown in figure. When a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the surface of the cavity. R can be determined by the equation :$ (1) $(R^{2} - R + 1) (2 - R) = 1$ (2) $(R^{2} + R+- 1) (2-R) = 1$ (3) $(R^{2} - R - 1) (2 - R) = 1$ (4) $(R^{2} + R - 1) (2 - R) = 1$ 95. $A rigid ball of mass m strikes a rigid wall at 60º and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall in the ball will be$ (1) $\frac{mV}{3}$ (2) $mV$ (3) $2mV$ (4) $\frac{mV}{2}$ 96. $A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. the angular acceleration of the rod when it makes an angle θ with the vertical is$ (1) $\frac{2 g}{3 l} cos θ$ (2) $\frac{3 g}{2 l} s in θ$ (3) $\frac{2 g}{3 l} s in θ$ (4) $\frac{3 g}{2 l} cos θ$ 97. $A thin rod of length 'L' is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k (\frac{x}{L})^{n}, where n can be zero or any positive number. If the position x_{C M} of the centre of mass of the rod is plotted against 'n', which of the following graphs best approximates the dependence of x_{C M} on n ?$ (1) (2) (3) (4)