AP EAPCET 07-Jul-2022 Shift 1 Paper

Block stops on incline plane when its initial K.E is used in doing work against friction and partly it is converted into potential energy.

As angle of incline is given 45∘ so, distance covered on incline (s) is related to height of block (h) as,
⇒sin‌45∘=

h

s

or s=√2h
Let block covers a distance s over block and reaches up-to height h. Then,

Initial‌K.E‌of‌block=Work‌done‌against‌friction+Potential‌energy‌gained‌by‌block
⇒

1

2

mu2=µmg‌cos‌θ⋅s+mgh
⇒

1

2

mu2=µmg‌cos‌θ⋅√2⋅h+mgh
⇒h=

‌ 1 2 mu2

√2µmg‌cos‌θ+mg

Here, initial K.E=

1

2

mu2=100J
m=5‌kg,θ=45∘,g=10m∕ s2
So,
h=

100

√2×0.5×5×10× 1 √2 +5×10

=

100

50×1.5

=

4

3

Hence, distance covered over block, s=√2h
⇒s=

√2×4

3

m=

4√2

3

m