Question

99. Two particles having equal charges, but
masses are in the ratio 1:2, are placed in an
uniform electric field 'E' and allowed to
move simultaneously. The ratio of their
kinetic energies at any instant will be
(1)1:2 (2)2:1 (3)1:8 (4)8:1​

Answer 1

Answer:

Since charge on both particles is same and they are accelerated through the same voltage, work done by electric field will be same for both the charges so the increase in kinetic energy will be same. Assuming that charges started from rest, we have:

2

1

m

1

v

1

2

=qV=

2

1

m

2

v

2

2

⇒

v

2

2

v

1

2

=

m

1

m

2

where V is the potential difference through which the charges are accelerated.

The magnetic force only provides the necessary centripetal force for circular motion:

R

1

m

1

v

1

2

=Bqv

1

R

2

m

2

v

2

2

=Bqv

2

⇒

R

2

R

1

=

m

2

v

2

m

1

v

1

=

m

2

0.5

m

1

0.5

⇒

m

2

m

1

=

R

2

2

R

1

2

Answer 2

The ratio of kinetic energies of the two particles is 1:2. (Option a)

Given:

Two particles have equal charges.

The masses are in the ratio of 1:2

To Find:

The ratio of their kinetic energies at any instant.

Solution:

We can simply solve this problem by using the following process.

The kinetic energy of a particle = $\frac{1}{2} mv^{2}$

It is given that the charges do not change, hence v is the same for both particles.

Also, the masses of the two particles are in the ratio of 1:2

Let mass = x

Then,

$m_{1} =x$ and $m_{2} =2x$

Now,

$KE_{1} :KE_{2} =\frac{1}{2} xv^{2}$ ÷ $\frac{1}{2} 2xv^{2}$

$KE_{1} :KE_{2} =\frac{\frac{1}{2}xv^{2} }{\frac{1}{2}2xv^{2} }}$

$KE_{1} :KE_{2} =\frac{1}{2}$

Hence, the ratio of kinetic energies of the two particles is 1:2.

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