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37. A block of mass m = 1 kg slides with velocity v=6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M = 2 kg, and length l = 1 m, the value of θ is approximately: (take g = 10 m/s²) (a) 63° (b) 55° (c) 69° (d) 49°
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36. A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre?
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35. A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be ______.
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34. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is : (a) m𝑙^2ω (b) 4m𝑙^2ω (c) 3m𝑙^2ω (d) 2m𝑙^2ω
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32. Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s⁻¹. The value of n, to the nearest integer, is _______. [Given: In one complete revolution, the disk rotates by 6.28 rad]
31. A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity ω. The angular momentum of M about point A is 𝐿_𝐴 which lies in the positive z direction and the angular momentum of M about point B is 𝐿_𝐵. The correct statement for this system is : (a) 𝐿_𝐴 is constant, both in magnitude and direction (b) 𝐿_𝐵 is constant in direction with varying magnitude (c) 𝐿_𝐴 and 𝐿_𝐵 are both constant in magnitude and direction (d) 𝐿_𝐵 is constant, both in magnitude and direction
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A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√𝑭 rad𝒔^(−𝟏). If F be the force exerted by the liquid at the other end then the value of x will be ____.
1. A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√𝑭 rad𝒔^(−𝟏). If F be the force exerted by the liquid at the other end then the value of x will be ____.
