The gravitational potential difference between the surface of a planet and a point 20 m above the surface, is 2 joule / kg. If the gravitational field is uniform, then the work done in carrying a 5 kg body to a height of 4 m above the surface is

Question

The gravitational potential difference between the surface of a planet and a point 20 m above the surface, is 2 joule / kg. If the gravitational field is uniform, then the work done in carrying a 5 kg body to a height of 4 m above the surface is (A) 2 J  (B) 20 J (C) 40 J (D) 10 J

Tardigrade Admin · Accepted Answer

Δ U=mg Δ h Δ V=(Δ U/m)=g Δ h ⇒ (2 J / kg )=g(20 m ) and Δ V'=g(4 m ) ; (Δ V'/2)=(4/20) Δ V=(4 × 2/20)=0.4 ( J / kg ) W ex =m Δ V'=(5 kg ) × 0.4 ( J / kg )=2 J

Q. The gravitational potential difference between the surface of a planet and a point $20 m$ above the surface, is $2$ joule $/ k g$ . If the gravitational field is uniform, then the work done in carrying a $5 k g$ body to a height of $4 m$ above the surface is

$2 J$

$20 J$

$40 J$

$10 J$

$Δ U = m g Δ h$
$Δ V = \frac{Δ U}{m} = g Δ h$
$\Rightarrow \frac{2 J}{k g} = g (20 m)$
and $Δ V^{'} = g (4 m); \frac{Δ V ^{'}}{2} = \frac{4}{20}$
$Δ V = \frac{4 \times 2}{20} = 0.4 \frac{J}{k g}$
$W_{e x} = m Δ V^{'} = (5 k g) \times 0.4 \frac{J}{k g} = 2 J$

Q. The gravitational potential difference between the surface of a planet and a point 20m above the surface, is 2 joule /kg. If the gravitational field is uniform, then the work done in carrying a 5kg body to a height of 4m above the surface is

2J

20J

40J

10J