MCQ
A block slides down a smooth inclined plane when released from the top, while another falls freely from the same point
  • A
    sliding block will reach the ground first with greater speed
  • B
    freely falling block will reach the ground first with greater speed
  • C
    both the blocks will reach the ground at the same time but with different speeds
  • both the blocks will reach the ground with same speed but the freely falling block first

Answer

Correct option: D.
both the blocks will reach the ground with same speed but the freely falling block first
d
In case of sliding motion on an inclined plane,

${\mathrm{h}=\mathrm{s}=\frac{1}{2} \mathrm{g} \sin \theta \mathrm{t}^{2}}$

${\text { or } \mathrm{t}=\mathrm{t_s}=\frac{1}{\sin \theta} \sqrt{\frac{2 \mathrm{h}}{\mathrm{g}}}}$

${\text { and } \mathrm{u}_{\mathrm{s}}=\sqrt{2 \mathrm{gh}}=\sqrt{2(\mathrm{g} \sin \theta) \mathrm{s}}}$

while in case of free fall,

$\mathrm{t}_{\mathrm{F}}=\sqrt{\frac{2 \mathrm{h}}{\mathrm{g}}}$ and $\mathrm{u}_{\mathrm{F}}=\sqrt{2 \mathrm{gh}}$

$\frac{\mathrm{t}_{\mathrm{F}}}{\mathrm{t}_{\mathrm{s}}}=\sin \theta<1 \mathrm{i.e.}, \mathrm{t}_{\mathrm{F}}<\mathrm{t}_{\mathrm{s}}$

i.e., falling body reaches the ground first.

Also $\quad \frac{\mathrm{u}_{\mathrm{F}}}{\mathrm{u}_{\mathrm{s}}}=1,$ i.e., $\mathrm{u}_{\mathrm{F}}=\mathrm{u}_{\mathrm{s}}$

i.e., both reach the ground with same speed (not velocity as for falling body direction is vertical while for sliding body along the plane downwards).

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