Question

Two bodies of masses m1 and m2 are dropped from height h1 and h2 respectively. They reach the ground after time t1 and t2 respectively. Which of the following relation is correct ? (A) 1/ 2 2 1 2 1 h h t t        (B)         2 1 2 1 h h t t (C) 2 1 2 1 2 1 m m t t        (D) 2 1 2 1 m m t t 

Answer 1

for first body of mass m1

a=g

distance travelled=h1

time taken to reach the ground =t1

since the motion is uniformly accelerated,so,we can use the Newton's eqaution

from third law

V^2=u^2+2gh.....i)

V^2=0^2+2×10×h1.....(at max. velocity, initial velocity will be zero)

for seconnd body

Using the same eqaution

V'^2=0+2gh2

V'^2=2gh2.....ii)

V^2/V'^2=2gh1/2gh2

V^2/V'^2=h1/h2....iv)

This will be the relation between,final velocities and height of the two bodies

Now let's find the relation between their time

for first body

V=u+at

V=gt1...iii)

for second body

V'=u+gt.....

V'=gt2......iv)

divideing equation ,III) from iv)

V/V'=t1/t2

from fourth we can say that

t1/t2=√h1/√h2

This is the relation between their time.....

{hope it helps}

Answer 2

The correct options are (A) and (C).

Two bodies of masses m₁ and m₂ are dropped from height h₁ and h₂ respectively. They reach the ground after time t₁ and t₂ respectively.

Which of the following relation is correct ?

1. $\frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}$
2. $\frac{t_1}{t_2}=\sqrt{\frac{h_2}{h_1}}$
3. $\frac{v_1}{v_2}=\sqrt{\frac{h_1}{h_2}}$
4. $\frac{v_1}{v_2}=\frac{h_2}{h_1}$

If a body drops from a height, initial velocity of the body will be zero.

using formula,

$\quad s=ut+\frac{1}{2}at^2$

∴ Time taken by the first body to reach the ground from height h₁ is given by,

$\implies t_1=\sqrt{\frac{2h_1}{g}}$

Similarly the time taken by the 2nd body to reach the ground from height h₂ is given by,

$\implies t_2=\sqrt{\frac{2h_2}{g}}$

∴ The relation between times and heights of bodies is ;

$\implies\frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}$

Also using formula, v² = u² + 2as

Final velocity of the first body is given by,

$\implies v_1=\sqrt{2gh_1}$

Similarly final velocity of the 2nd body is given by,

$\implies v_2=\sqrt{2gh_2}$

Now the relation between velocities and heights of bodies is ;

$\frac{v_1}{v_2}=\sqrt{\frac{h_1}{h_2}}$

Therefore options (A) & (C) both are correct.

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