IMO Practice Test: Gravitation | Class 9 Physics

Question 1 of 14

If both masses are doubled and the distance between them is halved, the gravitational force becomes:

2 times

4 times

8 times

16 times

Explanation: Masses give $2\times2 = 4$; halving $r$ gives $1/(1/2)^2 = 4$; total $4 \times 4 = 16$.

Question 2 of 14

A planet has the same mass as Earth but half its radius. Its surface $g$ compared with Earth's is:

half

the same

twice

four times

Explanation: $g = GM/R^2$; halving $R$ gives $1/(1/2)^2 = 4$ times the value.

Question 3 of 14

A ball thrown up returns to the thrower's hand. Its displacement and the sign of acceleration during the upward trip are:

zero displacement; $a$ downward throughout

maximum displacement; $a$ upward

zero displacement; $a$ zero

negative displacement; $a$ upward

Explanation: Over the full flight displacement is zero; gravity acts downward the whole time.

Question 4 of 14

A stone dropped from rest falls $H$ in the last second of an $n$-second fall is largest because:

speed is constant

the stone covers more distance each second as it speeds up

air resistance grows

$g$ increases with time

Explanation: Under constant $g$, distance per second increases as velocity builds up.

Question 5 of 14

An astronaut's mass is $70\ \text{kg}$. On a planet where $g = 25\ \text{m/s}^2$, the astronaut's weight is:

$70\ \text{N}$

$700\ \text{N}$

$1750\ \text{N}$

$2.8\ \text{N}$

Explanation: $W = mg = 70 \times 25 = 1750\ \text{N}$.

Question 6 of 14

Two cubes of equal mass but different volumes are dropped in water; the one that floats higher is the one with:

the larger volume (lower density)

the smaller volume (higher density)

the darker colour

the rougher surface

Explanation: Same mass, larger volume means lower density, so it floats higher.

Question 7 of 14

A block of relative density $0.8$ floats in water. The fraction of its volume above the surface is:

$0.2$

$0.8$

$0.5$

$1.0$

Explanation: Submerged fraction $= 0.8$, so $1 - 0.8 = 0.2$ is above the surface.

Question 8 of 14

A liquid has relative density $1.25$. Its density in SI units is:

$1.25\ \text{kg/m}^3$

$125\ \text{kg/m}^3$

$1250\ \text{kg/m}^3$

$12500\ \text{kg/m}^3$

Explanation: $\rho = 1.25 \times 1000 = 1250\ \text{kg/m}^3$.

Question 9 of 14

Why does the same nail sink in water but a needle can rest on the surface only due to surface tension, not buoyancy? Because for the nail:

density is less than water's

density is greater than water's so weight exceeds upthrust

the buoyant force is zero

$g$ is zero

Explanation: The nail's density exceeds water's, so its weight beats the buoyant force.

Question 10 of 14

A body of volume $200\ \text{cm}^3$ is fully immersed in water. The buoyant force on it is (take $g = 10\ \text{m/s}^2$, $\rho_w = 1000\ \text{kg/m}^3$):

$0.2\ \text{N}$

$2\ \text{N}$

$20\ \text{N}$

$200\ \text{N}$

Explanation: $V = 200\ \text{cm}^3 = 2 \times 10^{-4}\ \text{m}^3$; upthrust $= \rho V g = 1000 \times 2\times10^{-4} \times 10 = 2\ \text{N}$.

Question 11 of 14

A stone takes $4\ \text{s}$ to reach the ground when dropped from a cliff. The cliff's height is (take $g = 10\ \text{m/s}^2$):

$40\ \text{m}$

$80\ \text{m}$

$160\ \text{m}$

$20\ \text{m}$

Explanation: $h = \tfrac12 g t^2 = \tfrac12 (10)(16) = 80\ \text{m}$.

Question 12 of 14

Where would a given object weigh the most?

at the equator

at the North Pole

on top of Mount Everest

in a deep mine

Explanation: $g$ is largest at the poles (smallest $R$), so weight is greatest there.

Question 13 of 14

A hydrometer floats deeper in a liquid of:

higher density

lower density

higher temperature only

equal density to itself

Explanation: In a less dense liquid more volume must be submerged to get enough upthrust, so it floats deeper.

Question 14 of 14

An object is in 'weightlessness' inside a freely falling lift because:

its mass becomes zero

gravity switches off

both the object and the lift accelerate downward at $g$, so the floor exerts no normal force

air resistance lifts it

Explanation: In free fall the support force vanishes, giving the sensation of weightlessness; mass and $g$ are unchanged.

IMO Practice Test — Gravitation