Centre of Mass & Momentum PYQs Set 2 (PDF)

Set 2 of 4 · Questions 31-60 of 97

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Mere Teacher · Previous Year Questions NEET Physics · Centre of Mass & Momentum · Set 2 (Q31-60)
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31. $A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3 . The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m / s each. The velocity of the heavier fragment is____m / s .$ (1) $12$ (2) $102$ (3) $242$ (4) $122$ 32. $A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?$ (1) $1 J$ (2) $3 J$ (3) $30 kJ$ (4) $2 J$ 33. $Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be$ (1) $0.3 m/s and 0.5 m/s$ (2) $- 0.5 m/s and 0.3 m/s$ (3) $0.5 m/s and - 0.3 m/s$ (4) $- 0.3 m/s and 0.5 m/s$ 34. $Four particles A, B, C, D of mass \frac{m}{2}, m, 2 m, 4 m, have same momentum, respectively. The particle with maximum kinetic energy is:$ (1) $B$ (2) $A$ (3) $D$ (4) $C$ 35. $A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:$ (1) $\frac{3}{4}$ (2) $\frac{4}{3}$ (3) $\frac{5}{2}$ (4) $\frac{2}{5}$ 36. $Which of the following statements regarding centre of mass is NOT true?$ (1) $For two particles of equal mass, the centre of mass lies exactly midway between them$ (2) $For three non-linear particles of equal mass, the centre of mass coincides with the centroid of the triangle formed by the particles$ (3) $When the total external force on a system is zero, the velocity of the centre of mass of the system remains constant.$ (4) $For two particles of different masses, the centre of mass of the particles is nearer to the particle of lesser mass.$ 37. $An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x = +2m, its velocity is -4 j^m / s. The object's velocity (v) and acceleration (a) at x = -2 m will be$ (1) $v = 4 i^m/s, a = 8 j^m/ s^{2}$ (2) $v = 4 j^m / s, a = 8 i^m / s$ (3) $v = -4 j^m / s, a = 8 i^m / s^{2}$ (4) $v = -4 i^m /s, a = -8 j^m/ s^{2}$ 38. $A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is :$ (1) $\frac{W d}{x}$ (2) $\frac{W ( d - x )}{χ}$ (3) $\frac{W ( d - x )}{d}$ (4) $\frac{W x}{d}$ 39. $As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break?$ (1) $A$ (2) $B$ (3) $C$ (4) $D$ 40. $An object flying in air with velocity (20 i + 25 j - 12 k) suddenly breaks in two pieces whose masses are in the ratio 1 : 5 . The smaller mass flies off with a velocity (100 i + 35 j + 8 k) . The velocity of the larger piece will be [NEET 2019]$ (1) $4 i + 23 j - 16 k$ (2) $- 100 i - 35 j - 8 k$ (3) $20 i + 15 j - 80 k$ (4) $- 20 i - 15 j - 80 k$ 41. $The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b, whose mass per unit area (σ) varies as σ = \frac{σ _{0} x}{ab} (where σ_{0} is a constant), would be fig-x$ (1) $(\frac{2}{3} a, \frac{b}{2})$ (2) $(\frac{a}{2}, \frac{b}{2})$ (3) $(\frac{1}{3} a, \frac{b}{2})$ (4) $(\frac{2}{3} a, \frac{2}{3} b)$ 42. $Two spherical bodies of mass M and 5 M and radii R and 2R released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:$ (1) $4.5 R$ (2) $7.5 R$ (3) $1.5 R$ (4) $2.5 R$ 43. $The mass of a hydrogen molecule is 3.32 \times 1 0^{-27} kg. If 1 0^{23} hydrogen molecules strike, per second, a fixed wall of area 2 c m^{2} at an angle of 45° to the normal, and rebound elastically with a speed of 1 0^{3} m/s, then the pressure on the wall is nearly :$ (1) $2.35 \times 1 0^{2} N/ m^{2}$ (2) $4.70 \times 1 0^{2} N/ m^{2}$ (3) $2.35 \times 1 0^{3} N/ m^{2}$ (4) $4.70 \times 1 0^{3} N/ m^{2}$ 44. $The centre of mass of a homogenous semi-circular plate of radius r is located at A as shown in the figure. The distance OA is$ (1) $\frac{r}{3}$ (2) $\frac{2 r}{3}$ (3) $\frac{r}{2}$ (4) $None$ 45. $Three identical spheres each of diameter 23 m are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the sphere is removed, then the shift in the position of the centre of mass of the system is$ (1) $12 m$ (2) $1 m$ (3) $2 m$ (4) $3 2 m$ 46. $Two objects of masses 10 kg and 20 kg, respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is [NEET 2022]$ (1) $\frac{20}{3} m$ (2) $10 m$ (3) $5 m$ (4) $\frac{10}{3} m$ 47. $A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is$ (1) $190 g$ (2) $200 g$ (3) $300 g$ (4) $290 g$ 48. $A light rod of length l has two masses m_{1} and m_{2} attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is$ (1) $\frac{m _{1} m _{2}}{m _{1} + m _{2}} l^{2}$ (2) $\frac{m _{1} m _{2}}{m _{1} + m _{2}}$ (3) $(m_{1} + m_{2}) f^{2}$ (4) $m_{1} m_{2} l^{2}$ 49. $A thin uniform rod (X) of mass M and length L is pivoted at a height (\frac{L}{3}) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is____. (g = gravitational acceleration)$ (1) $\frac{3}{2} \frac{g}{L}$ (2) $\frac{1}{2} \frac{g}{L}$ (3) $\frac{3}{2} \frac{g}{L}$ (4) $\frac{3 g}{L}$ 50. $A semicircular plate of mass m has radius r and centre c. The centre of mass of the plate is at a distance x from its centre c . Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is$ (1) $\frac{m r ^{2}}{2}$ (2) $\frac{m r ^{2}}{4}$ (3) $\frac{m r ^{2}}{2} + m x^{2}$ (4) $\frac{m r ^{2}}{2} - m x^{2}$ 51. $Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be$ (1) $2.0 cm$ (2) $1.5 cm$ (3) $1.0 cm$ (4) $0.5 cm$ 52. $A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A . The normal reaction on A is$ (1) $\frac{W ( d - x )}{x}$ (2) $\frac{W ( d - x )}{d}$ (3) $\frac{Wx}{d}$ (4) $\frac{Wd}{x}$ 53. $A bullet of 10 g leaves the barrel of gun with a velocity of 600 m s^{- 1} . If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be:$ (1) $6Ns$ (2) $3Ns$ (3) $36 Ns$ (4) $12 Ns$ 54. $A bullet of mass 25 g moves horizontally at a speed of 250 m / s is fired into a wooden block of mass 1 kg suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of the mass of the block rises through a height of 20 cm . The speed of the bullet as it emerges from the block is (take, g = 10 m / s^{2})$ (1) $300 m / s$ (2) $220 m / s$ (3) $150 m / s$ (4) $170 m / s$ 55. $A solid cylinder of mass M and radius R rolls down an inclined plane of length L and height h, without slipping. Find the speed of its centre of mass when the cylinder reaches its bottom.$ (1) $2 gh$ (2) $\frac{3 gh}{4}$ (3) $\frac{4 gh}{3}$ (4) $4 gh$ 56. $Point masses m1 and m2 are placed at the opposite ends of a rigid of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω0 is minimum, is given by :$ (1) $x = \frac{m _{1}}{m _{2}} L$ (2) $x = \frac{m _{2}}{m _{1}} L$ (3) $x = \frac{m _{2} L}{m _{1} + m _{2}}$ (4) $x = \frac{m _{1} L}{m _{1} + m _{2}}$ 57. $Two blocks of equal masses are tied to the ends of a light string. The string passes over a mass less pulley fixed on frictionless surface as shown in the figure. The acceleration of the centre of mass of the blocks is (g - acceleration due to gravity)$ (1) $(\frac{3 - 1}{4 2}) g$ (2) $(\frac{3 1}{4 2})$ (3) $(\frac{3 - 1}{2 2}) g$ (4) $(\frac{3 + 1}{2 2}) g$ 58. $A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination 30º. The centre of mass of the cylinder has speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, [take g = 10 m/ s^{2}]$ (1) $2.2 m$ (2) $1.6 m$ (3) $1.2 m$ (4) $2.4 m$ 59. $Three identical spheres each of mass 1 kg are placed touching one another with their centres in a straight line. Their centres are marked as A, B, C respectively. The distance of centre of mass of the system from A is$ (1) $\frac{AB + AC}{2}$ (2) $\frac{AB + BC}{2}$ (3) $\frac{AC - AB}{3}$ (4) $\frac{AB + AC}{3}$ 60. $A small disc of mass 500 g and radius 5 cm rolls down an inclined plane without slipping. Speed of its centre of mass when it reaches the bottom of the inclined plane depends on$ (1) $mass and radius$ (2) $mass and height of the incline$ (3) $height of the incline$ (4) $height of the incline and acceleration due to gravity$