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First Year Physics Vectors and Equilibrium


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Class 9Class 10First YearSecond Year
Canyouaddzerotoanullvector?Can you add zero to a null vector?

A uniform beam of 200 \mathrm{~N} is supported horizontally as shown. If the breaking stress of the rope is 400 \mathrm{~N} how far can the man of weight 400 \mathrm{~N} walk from point A on the beam as shown in figure?
A uniform beam of  200 \mathrm{~N}  is supported horizontally as shown. If the breaking stress of the rope is  400 \mathrm{~N}  how far can the man of weight  400 \mathrm{~N}  walk from point  A  on the beam as shown in figure?

Auniformbeamof200 Nissupportedhorizontallyasshown.Ifthebreakingstressoftheropeis400 Nhowfarcanthemanofweight400 NwalkfrompointAonthebeamasshowninfigure?A uniform beam of 200 \mathrm{~N} is supported horizontally as shown. If the breaking stress of the rope is 400 \mathrm{~N} how far can the man of weight 400 \mathrm{~N} walk from point A on the beam as shown in figure?

Show that the three vectors \hat{i}+\hat{j}+\hat{k} 2 \hat{i}-3 \hat{j}+\hat{k} and 4 \hat{i}+\hat{j}-5 \hat{k} are mutually perpendicular.
Show that the three vectors  \hat{i}+\hat{j}+\hat{k} 2 \hat{i}-3 \hat{j}+\hat{k}  and  4 \hat{i}+\hat{j}-5 \hat{k}  are mutually perpendicular.

Showthatthethreevectorsi^+j^+k^2i^3j^+k^and4i^+j^5k^aremutuallyperpendicular.Show that the three vectors \hat{i}+\hat{j}+\hat{k} 2 \hat{i}-3 \hat{j}+\hat{k} and 4 \hat{i}+\hat{j}-5 \hat{k} are mutually perpendicular.

PROBLEM 2.18A uniform sphere of weight 10 \mathrm{~N} is held by a string attached to a frictionless wall so that the string makes an angle of 30^{\circ} with the wall. Find the tension in the string and the force exerted on the sphere by the wall.
PROBLEM 2.18A uniform sphere of weight  10 \mathrm{~N}  is held by a string attached to a frictionless wall so that the string makes an angle of  30^{\circ}  with the wall. Find the tension in the string and the force exerted on the sphere by the wall.

PROBLEM2.18Auniformsphereofweight10 Nisheldbyastringattachedtoafrictionlesswallsothatthestringmakesanangleof30withthewall.Findthetensioninthestringandtheforceexertedonthespherebythewall.PROBLEM 2.18A uniform sphere of weight 10 \mathrm{~N} is held by a string attached to a frictionless wall so that the string makes an angle of 30^{\circ} with the wall. Find the tension in the string and the force exerted on the sphere by the wall.

Identify the correct answer:(ii) A horizontal force F is applied to a small object P of mass m at rest on a smooth plane inclined at an angle \theta to the horizontal as shown in figure. The magnitude of the resultant force acting up and along the surface of the plane on the object is:(a) F \cos \theta-\mathrm{mg} \sin \theta (b) \mathrm{F} \sin \theta-\mathrm{mg} \cos \theta (c) F \cos \theta+m g \cos \theta (d) F \sin \theta+m g \sin \theta (e) m g \tan \theta
Identify the correct answer:(ii) A horizontal force  F  is applied to a small object  P  of mass  m  at rest on a smooth plane inclined at an angle  \theta  to the horizontal as shown in figure. The magnitude of the resultant force acting up and along the surface of the plane on the object is:(a)  F \cos \theta-\mathrm{mg} \sin \theta (b)  \mathrm{F} \sin \theta-\mathrm{mg} \cos \theta (c)  F \cos \theta+m g \cos \theta (d)  F \sin \theta+m g \sin \theta (e)  m g \tan \theta

Identifythecorrectanswer:(ii)AhorizontalforceFisappliedtoasmallobjectPofmassmatrestonasmoothplaneinclinedatanangleθtothehorizontalasshowninfigure.Themagnitudeoftheresultantforceactingupandalongthesurfaceoftheplaneontheobjectis:(a)Fcosθmgsinθ(b)Fsinθmgcosθ(c)Fcosθ+mgcosθ(d)Fsinθ+mgsinθ(e)mgtanθIdentify the correct answer:(ii) A horizontal force F is applied to a small object P of mass m at rest on a smooth plane inclined at an angle \theta to the horizontal as shown in figure. The magnitude of the resultant force acting up and along the surface of the plane on the object is:(a) F \cos \theta-\mathrm{mg} \sin \theta (b) \mathrm{F} \sin \theta-\mathrm{mg} \cos \theta (c) F \cos \theta+m g \cos \theta (d) F \sin \theta+m g \sin \theta (e) m g \tan \theta

Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.
Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.

Showthatthesumanddifferenceoftwoperpendicularvectorsofequallengthsarealsoperpendicularandofthesamelength.Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.

The magnitude of dot and cross products of two vectors are 6 \sqrt{3} and 6 respectively. Find the angle between the vector.
The magnitude of dot and cross products of two vectors are  6 \sqrt{3}  and 6 respectively. Find the angle between the vector.

Themagnitudeofdotandcrossproductsoftwovectorsare63and6respectively.Findtheanglebetweenthevector.The magnitude of dot and cross products of two vectors are 6 \sqrt{3} and 6 respectively. Find the angle between the vector.

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