Two light rods AB and BC of length $$1.0$$ m each are hinged together as shown in fig. Rod AB makes an angle θ with vertical while rod BC makes an angle ϕ with horizontal. End C of rod BC remains in contact with horizontal. Rod AB is rotated about A with constant angular velocity ω$$=1$$ $$rad/s$$ in clockwise direction. At the instant when θ$$=300$$ and ϕ$$=300$$. Match the variables in column I with values in column II.

Question

Two light rods AB and BC of length $$1.0$$ m each are hinged together as shown in fig. Rod AB makes an angle θ with vertical while rod BC makes an angle ϕ with horizontal. End C of rod BC remains in contact with horizontal. Rod AB is rotated about A with constant angular velocity ω$$=1$$  $$rad/s$$ in clockwise direction. At the instant when θ$$=300$$ and ϕ$$=300$$. Match the variables in column I with values in column II.

Infinity Learn · Accepted Answer

$$A)$$  From figure, $$l($$$$cos$$⁡θ$$+$$$$sin$$⁡ϕ$$)=$$ constant $$($$−$$sin$$⁡θ$$)d$$θ$$dt+($$$$cos$$⁡ϕ$$)d$$ϕ$$dt=0($$−$$sin$$⁡$$30)$$ω$$+($$$$cos$$⁡$$30)$$ω′$$=0$$⇒−$$12+32$$ω′$$=0$$⇒ω′$$=13B)$$ $$x=l($$$$sin$$⁡θ$$+$$$$cos$$⁡ϕ$$)VD=VC=dxdt=l($$$$cos$$⁡θ$$)d$$θdt−$$($$$$sin$$⁡ϕ$$)d$$ϕ$$dt=(1)32(1)$$−$$1213=3$$−$$123=13$$ ω′$$=$$ω$$sin$$⁡θ$$cos$$⁡ϕ$$C)$$ From A,α′$$=d$$ω′$$dt=$$ω$$cos2$$⁡ϕ$$($$$$cos$$⁡ϕ$$)($$$$cos$$⁡θ$$)$$ω$$+($$$$sin$$⁡θ$$)($$$$sin$$⁡ϕ$$)$$ω′$$=4332$$⋅$$32$$⋅$$1+12$$⋅$$12$$⋅$$13=33+133D)$$ $$aB=l$$ω$$2=112=1$$

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