Motion in a Plane Easy Questions and Answers

When a vector is multiplied with a scalar, the result is a vector.

Correct Option: C

When a vector is multiplied with a scalar, the result is a vector.

(A^{^→} + B^{^→})² = (C^{^→})²
⇒ A² + B² + 2 A^{^→}.B^{^→} = C²
⇒ 3² + 4² + 2 A^{^→}.B^{^→} = 5²
⇒ 2 A^{^→}.B^{^→} = 0
⇒ A^{^→}.B^{^→} = 0
∴ A^{^→} ⊥ B^{^→}
Here A² + B² = C².
Hence, A^{^→} ⊥ B^{^→}

Correct Option: A

Note that (B^{^→} × A^{^→}) ⊥ A^{^→} . Hence their dot product is zero.

Correct Option: B

Note that (B^{^→} × A^{^→}) ⊥ A^{^→} . Hence their dot product is zero.

r^{^→} = (a cos ωt)î + (a sin ωt)ĵ

v^{^→} =	dr^{^→}	=	d	{ (a cos ωt)î + (a sin ωt)ĵ }
	dt		dt

= (-aω sin ωt)î + (aω cos ωt)ĵ
= ω [ (-a sin ωt)î + (a cos ωt)ĵ ]

Slope of position vector =	a sin ωt	= tan ωt
	a cos ωt

& slope of velocity vector =	-a cos ωt	=	-1
	a sin ωt		tan ωt

∴ velocity is perpendicular to the displacement.

Correct Option: D

r^{^→} = (a cos ωt)î + (a sin ωt)ĵ

v^{^→} =	dr^{^→}	=	d	{ (a cos ωt)î + (a sin ωt)ĵ }
	dt		dt

= (-aω sin ωt)î + (aω cos ωt)ĵ
= ω [ (-a sin ωt)î + (a cos ωt)ĵ ]

Slope of position vector =	a sin ωt	= tan ωt
	a cos ωt

& slope of velocity vector =	-a cos ωt	=	-1
	a sin ωt		tan ωt

∴ velocity is perpendicular to the displacement.

Let after 1 sec angle become 60°. When the end A moves by 10 m left, the end B moves upward by BB′ = 10 × √3 = 10 × 1.73 = 17.3 m / s

Correct Option: D

Let after 1 sec angle become 60°. When the end A moves by 10 m left, the end B moves upward by BB′ = 10 × √3 = 10 × 1.73 = 17.3 m / s

Motion in a Plane

Motion in a Plane

Mechanics

Correct Option: C

Correct Option: A

Correct Option: B

Correct Option: D

Correct Option: D