Verified Solution • 2025–26 Session moderate

QJEEM22Ph8f4e: JEE Main 2022 Physics - Class 11 JEEM22Ph8f4e Solution: A block 'A' takes 2 s to slide down a frictionless incline of…

A block 'A' takes 2 s to slide down a frictionless incline of 30 ∘^\circ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45 ∘^\circ , the time taken by the block, to slide down the incline, will be approximately :

Multiple Choice Options

  • A 2.66 s
  • B 0.83 s
  • C 1.68 s
  • D 0.70 s

Step-by-Step Verified Solution

θ1=30∘, θ2=45∘{\theta _1} = 30^\circ ,\,{\theta _2} = 45^\circ

a1=gsin⁡θ1=5{a_1} = g\sin {\theta _1} = 5 m/s2, a2=gsin⁡θ2=52{a_2} = g\sin {\theta _2} = 5\sqrt 2 m/s2

t1t2=2la12la2=a2a1{{{t_1}} \over {{t_2}}} = {{\sqrt {{{2l} \over {{a_1}}}} } \over {\sqrt {{{2l} \over {{a_2}}}} }} = \sqrt {{{{a_2}} \over {{a_1}}}}

t1t2=(2)1/4{{{t_1}} \over {{t_2}}} = {(2)^{1/4}}

t2=(2)3/4{t_2} = {(2)^{3/4}}

≈1.68\approx 1.68 s

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