Question

3 Mark Questions (Numencal)
16. A force acting on a 20 kg mass changes its velocity from 5m/s to 2 m/s Calculate the work done
217. The KE of an object of mass m moving with a velocity of 5m/s is 25 J. What will be its KE when its velocrty is doubled? What will be its KE when its
velocity is increased 3 times?
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Answer 1

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16) Here, we have to find the work done by the object but Force and displacement is not given. But the mass and change in velocity is given. We know that according to work-energy theroam:

• Work done = Change in Kinetic energy

Given:

• Mass of the body = 20 kg
• Final velocity is 2 m/s
• Initial velocity was 5 m/s

By using formula,

⇛ W = 1/2 m(v² - u²)

Plugging the given values,

⇛ W = 1/2 × 20 × (2² - 5²)

⇛ W = 10(4 - 25)

⇛ W = -210 J

Thus, the work done by the object is -210 J and here negative sign represents opposite direction.

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17) Before solving the question, Let's checkout the formula of Kinetic energy which is energy possessed by a body in virtue of its motion:

• Kinetic energy = 1/2 × mass × velocity²

The KE is directly proportional to the square of velocity. That means, if velocity is doubled them KE becomes 4 times and if it is tripled, it becomes 9 times.

• Initial Kinetic energy = 25 J

After being Doubled:

⇛ Final Kinetic energy = 25 × 4 = 100 J

After being tripled:

⇛ Final Kinetic energy = 25 × 9 = 225 J

Answer 2

Explanation:

Question 1 )

Given : -

• mass = 20 kg
• initial velocity (u) = 5 m/sec
• final velocity (v) = 2 m/sec

• time (t)= 1sec

Solution : -

so , from first equation of motion

v= u+ at

or, a= ( v- u) / t

a= ( 2 ms-¹ - 5 ms-¹) / 15

a= - 3 ms-²

therefore, from third equation of motion

v²- u²= 2as

= ( 2ms -1 )² - ( 5ms-¹) ²

= 2× (-3ms-²) ×5

= -21 m²s² = -6ms-²× 5

= s = 7/2 metre

therefore, we know ,

workdone= f × s

and , F = m× a

so, work = m× a× s

= 20 kg × ( -3ms-²) × 7/2m

= - 210 joules.

Hence the answer is - 210

Question ( 2 )

Given : -

• v = 5m/s
• K.E = 25 J

Solution : -

K.E = 1/2 mv^2

25 = 1/2 m (5)^2

25 x 2 = 25m

m = 2 kg

Now if the velocity becomes 3 times then the velocity is 3 x 5 = 15m/S

Now new K.E = 1/2 x 2 x 15^2

= 225 J

Answer is 225 j