A uniform rod is pivoted to a trolley as shown in figure. Let α₁ be the angular acceleration of rod with respect to trolley when the trolley is moving with uniform velocity V₀ and α₂ be the angular acceleration of the rod with respect to trolley when the trolley is moving with uniform acceleration a₀ so that α⃗₂ = −α⃗₁. Then 2a₀/g = ...
Physics · Mixed Chapter
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Question

A uniform rod is pivoted to a trolley as shown in figure. Let α₁ be the angular acceleration of rod with respect to trolley when the trolley is moving with uniform velocity V₀ and α₂ be the angular acceleration of the rod with respect to trolley when the trolley is moving with uniform acceleration a₀ so that α⃗₂ = −α⃗₁. Then 2a₀/g = ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a rod inclined at 53°, gravity creates clockwise torque about the pivot τ_g=−Mg(L/2)cos53°. In uniform translation, its angular acceleration α₁ is proportional to −g cos53°. Step 2: In a trolley accelerating right at a₀, add the leftward pseudo-force Ma₀ at its centre of mass. The angular acceleration is proportional to −g cos53°+a₀ sin53°. Step 3: Given α₂=−α₁, set −g cos53°+a₀ sin53°=+g cos53°. Thus a₀=2g cot53°=2g(3/4)=3g/2. Step 4: 2a₀/g=3.