Newton's second law — F = ma (net force), impulse-momentum form: Question bank

1.2.2 · D5 · Physics › Newton's Laws & Dynamics › Newton's second law — F = ma (net force), impulse-momentum f

True ya false — justify karo

Constant velocity ka matlab hai ki object par zero net force act kar raha hai.

True. Constant velocity ⇒

a = 0

⇒

F_{net} = m a = 0

. Individual forces phir bhi exist kar sakte hain (woh bas cancel ho jaate hain), lekin unka vector sum zero hota hai.

Agar kisi body par net force zero hai, toh uska momentum change nahi ho sakta.

True.

F_{net} = \frac{d p}{d t} = 0

ka matlab hai

p

constant hai. Yahi Newton's First Law (Inertia) hai jo Second Law ke andar hi rehta hai.

Koi body ek instant par zero velocity rakhte hue bhi nonzero acceleration rakh sakti hai.

True. Ek throw ki gayi ball ki flight ke top par

v = 0

hota hai lekin gravity phir bhi act karti hai, isliye

a = g

neeche ki taraf — velocity momentarily zero hai phir bhi badalne wali hai.

Jo do objects equal momentum rakhte hain unki kinetic energy hamesha equal hoti hai.

False.

p = m v

lekin

K E = \frac{1}{2} m v^{2} = \frac{p ^{2}}{2 m}

. Fixed

p

ke liye, halka object zyada kinetic energy carry karta hai — dekho Work-Energy Theorem.

Kisi object ki speed double karne se uska momentum double hota hai lekin uski kinetic energy bhi double hoti hai.

Doosre hisse mein False. Momentum

m v

double hota hai, lekin

K E = \frac{1}{2} m v^{2}

chaar guna ho jaati hai kyunki yeh

v^{2}

par depend karti hai.

Impulse aur force ke units same hote hain.

False. Force N hai; impulse N·s = kg·m/s hai. Impulse woh force hai jo time ke saath accumulate hoti hai — yeh fundamentally alag quantity hai.

Ek bada force hamesha bada impulse produce karta hai.

False. Impulse

F Δ t

hai. Ek bada force bahut kam time ke liye act kare toh tiny impulse de sakta hai; ek gentle force ghanton tak act kare toh bahut bada impulse de sakta hai.

Constant-mass case mein, momentum form aur

F = ma

identical predictions dete hain.

True. Jab

\frac{d m}{d t} = 0

hota hai toh product rule

v \frac{d m}{d t}

term ko hata deta hai, aur exactly

F = m a

milta hai. Yeh tabhi alag hote hain jab mass change hota hai.

Vacuum mein bhaari objects zyada tezi se girte hain kyunki gravity unhe zyada kheenchti hai.

False. Weight

m g

bada hai, lekin inertia

m

bhi bada hai;

a = m g / m = g

mein mass cancel ho jaata hai. Sabhi masses

g

par accelerate karte hain.

Velocity ke perpendicular direction mein point karne wala force koi work nahi karta lekin phir bhi momentum change karta hai.

True. Momentum ek vector hai; ek sideways force uski direction change karta hai (isliye

Δ p \neq = 0

) jabki zero work karta hai kyunki yeh motion ke perpendicular hai.

Error pakdo

"Car chalti reh rahi hai, isliye koi forward force zaroor hoga jo ise push kar raha hai."

Error: "chalte rehna" ko "accelerate karna" samjha ja raha hai. Constant speed par engine ka push sirf drag/friction ko cancel karta hai; net force zero hai. Motion ko continue karne ke liye force ki zaroorat nahi (First Law) — sirf change karne ke liye chahiye.

F = ma

, isliye main rocket ka thrust mass times acceleration se compute kar sakta hoon."

Error: rocket mass kho raha hai, isliye

\frac{d m}{d t} \neq = 0

. Tumhe

F = \frac{d ( m v )}{d t} = m a + v \frac{d m}{d t}

use karna hoga; jo term chhooti hai wahi poora point hai (dekho Variable Mass Systems & Rocket Equation).

"Ball

20

m/s se

30

m/s doosri taraf gayi, isliye

Δ p = 10 m

hua."

Error: momentum ek vector hai. Initial direction ko

+

maano,

Δ p = m (- 30 - 20) = - 50 m

hoga, na ki

10 m

. Reversal mein sign aana hi chahiye.

"Friction ek force hai, isliye agar kisi block par sirf friction hai toh woh forward accelerate karega."

Error: friction motion ko oppose karta hai, isliye block decelerate hota hai; net force backward point karta hai, negative acceleration deta hai. Dekho Friction.

"Airbags driver ka momentum change reduce karte hain."

Error: jab initial aur final speeds set ho jaati hain toh

Δ p

fix ho jaata hai. Airbag time

Δ t

badhaata hai, isliye

F = Δ p /Δ t

chhota hota hai — momentum change unchanged rehta hai, force nahi.

"Kyunki impulse

Δ p

ke barabar hota hai, isliye zyada momentum wale object mein zyada impulse hota hai."

Error: impulse ek interval mein momentum ka change hota hai, na ki momentum khud. Ek fast object jo constant velocity par cruise kar raha hai uska

p

bahut bada hoga lekin impulse zero hoga.

"Newton's second law kehta hai ki force velocity cause karta hai."

Error: force acceleration cause karta hai (velocity/momentum ke change ki rate), velocity nahi. Ek body ke paas pehle se velocity hoti hai bina kisi force ke.

Why questions

Momentum form

\frac{d p}{d t}

m a

se "zyada fundamental" kyun maana jaata hai?

Kyunki yeh tab bhi valid rehta hai jab mass change hota hai (rockets, raindrops, conveyor belts).

m a

ek special case hai jo silently maan leta hai ki

\frac{d m}{d t} = 0

F_{net} = ma

mein sirf "force" ki jagah "net" force kyun specify karte hain?

Kyunki acceleration sirf saare forces ke vector sum par respond karta hai. Das forces jo cancel ho jaayein woh zero acceleration produce karte hain chahe har ek real ho.

Landing par ghutne modhna pair par force kyun reduce karta hai?

Yeh stopping time

Δ t

badhata hai. Kyunki

Δ p

tumhari landing speed se fix hoti hai, bada

Δ t

F = Δ p /Δ t

ko chhota karta hai.

Do bahut alag force-time graphs identical velocity change kyun produce kar sakte hain?

Velocity change sirf impulse

= \int F d t

= force–time curve ke neeche area par depend karta hai. Alag shapes jo equal area rakhein equal

Δ p

dete hain.

Newton's Third Law equation

F_{net} = ma

mein appear kyun nahi karta?

Kyunki

F_{net}

sirf is ek body par act karne wale forces count karta hai. Third-Law reaction doosri body par act karta hai, isliye yeh is object ki equation mein kabhi nahi aata — dekho Newton's Third Law.

Momentum ka conservation directly Second Law se kyun follow karta hai?

Agar

F_{net} = 0

toh

\frac{d p}{d t} = 0

, isliye

p

constant hai. Ek isolated system mein internal forces pairs mein cancel ho jaate hain — dekho Conservation of Linear Momentum.

Impulse force ka time-integral kyun hai jabki work–energy theorem space-integral use karta hai?

Impulse

\int F d t

track karta hai ki force time par kaise accumulate hoti hai (momentum change); work

\int F d x

track karta hai distance par accumulation (energy change). Same force, alag accountant — dekho Work-Energy Theorem.

Edge cases

Ek raindrop girate waqt grow karta hai bina kisi horizontal force ke; kya uska horizontal momentum constant rehta hai chahe woh slow down ho?

Haan.

F_{x} = 0

ke saath,

\frac{d ( m v _{x} )}{d t} = 0

, isliye

m v_{x}

conserved hai. Jaise

m

badhta hai,

v_{x}

ghatna chahiye —

ma

akela galat tarike se constant

v_{x}

predict karta.

Agar mass zero ho, toh

F = ma

kya predict karta hai, aur kya yeh physical hai?

Kisi bhi finite

F

ke liye infinite

a

ki demand karega (ya

F = 0

). Massless bodies is law se describe nahi hoti; yeh apne domain ke bahar ek degenerate case hai.

Ek instantaneous, ideal collision (

Δ t \to 0

) mein finite momentum change ke saath, force ka kya hoga?

Average force

F = Δ p /Δ t \to \infty

. Real contacts hamesha nonzero time lete hain, isliye "instantaneous" force ek idealisation hai — dekho Collisions and Elasticity.

Ek ball wall se same speed se bounce karti hai jis speed se aayi thi; kya uska momentum change zero hai kyunki speed unchanged hai?

Nahi. Momentum ek vector hai: yeh direction reverse karta hai, isliye

Δ p = 2 m v

magnitude mein. Sirf speed unchanged hai, momentum nahi.

Koi object ek aisi force experience karta hai jo hamesha uski velocity ke exactly perpendicular hai; uski long-term speed aur momentum behaviour kya hogi?

Speed constant rehti hai (zero work), lekin momentum continuously direction change karta hai — jaise uniform circular motion. Constant

∣ p ∣

, lekin

p

hamesha badalta rehta hai.

Ek complete oscillation mein ek spring ek block ko symmetrically aage-peechhe push karta hai; ek complete period mein net impulse kya hai?

Zero. Block apni starting velocity par wapas aata hai, isliye

Δ p = 0

, isliye total impulse (

F

–

t

ke neeche area) zero hai — positive aur negative halves cancel ho jaate hain.

Recall Ek-line survival kit

Teen questions pucho aur zyaadatar traps gayab ho jaate hain: (1) Is body par net force kya hai? (2) Kya mass change ho raha hai — kya mujhe $v \frac{d m}{d t}$ term chahiye? (3) Kya momentum yahaan ek vector hai — kya maine signs aur directions rakhe?

Connections

Newton's Second Law — F = ma (net force), impulse-momentum form — parent topic.
Newton's First Law (Inertia) — $F_{net} = 0$ ke traps.
Newton's Third Law — kyun reaction force is body ki equation mein kabhi nahi aata.
Conservation of Linear Momentum — zero-net-force ka consequence.
Collisions and Elasticity — reversal aur short- $Δ t$ edge cases.
Friction — "forward force" aur deceleration ke traps.
Variable Mass Systems & Rocket Equation — changing-mass edge cases.
Work-Energy Theorem — time- vs space-integral ka distinction.