Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

12 N,6 N
13 N, 5 N
10 N,8 N
16 N, 2 N

Solution

The linear velocity of a rotating body is given by :

\(\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r}\)

If \(\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r}\) and \(\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r}\), then the magnitude of \(\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r}\) is

\(\sqrt{29}\) units
\(\sqrt{31}\) units
\(\sqrt{37}\) units
\(\sqrt{41}\) units

Solution

A rectangular sheet of material has a width of 3 m and a length of 4 m. Forces with magnitudes of 3 N and 4N. respectively, are applied parallel to two edges of the sheet,as shown in the figure below.

A third force F,is applied to the centre of the sheet, along a line in the plane of the sheet, at an angle = tan 0.75 with respect to the horizontal direction. The sheet will be intranslational equilibrium when F has what value?

F = 3 N
F = 4N
F= 5N
F = 7N

Solution

A body is in translational equilibrium when the components of all external forces cancel.

For the sheet : F cos θ= 4 N, F sinθ= 3 N. The magnitude of F is found by adding the squares of the components:F² cos² θ+ F² sin² θ= F² = 4²+ 3²= 25 N². Therefore F= 5N.The F vector points in the proper direction,since tan θ= 0.75 = 3/4.

If A = B + C and the magnitudes of A, B and C are 5, 4 and 3 units, the angle between A and C is

cos^-1(3/5)
cos^-1(4/5)
^π⁄₂
sin^-1(3/4)

Solution

See fig. Clearly A is the resultant of B and C. Further B is perpendicular to C

cos θ= 3/5 or θ= cos^-1(3/5)

Two vectors A and B lie in a plane, another vector C lies out side this plane, then the resultant of these three vectors i.e., A+ B + C

can be zero
cannot be zero
lies in the plane containing A+ B
lies in the plane containing A– B

Out of the following sets of forces, the resultant of which cannot be zero?

10, 10, 10
10, 10, 20
10, 20, 20
10, 20, 40

Solution

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

√3
√2
√5
¹⁄_√2

A bomb is dropped from an aeroplane moving horizontally at constant speed. If air resistance is taken into consideration, then the bomb

falls on earth exactly below the aeroplane
falls on the earth exactly behind the aeroplane
falls on the earths ahead of the aeroplane
flies with the aeroplane

Solution

If there is no resistance, bomb will drop at a place exactly below the flying aeroplane. But when we take into account air resistance, bomb will face deceleration inits velocity. So,it will fall on the earth exactly behind the aeroplane.

A bucket, full of water is revolved in a vertical circle of radius 2 m. What should be the maximum time-period of revolution so that the water doesn’t fall out of the bucket?

1 sec
2 sec
3 sec
4 sec

Solution

A projectile of mass m is fired with velocity u making angle θ with the horizontal. Its angular momentum about the point of projection when it hits the ground is given by

\(\frac{2mu\, sin^{2}\theta cos\theta }{g}\)
\(\frac{2mu^{3}\, sin^{2}\theta cos\theta }{g}\)
\(\frac{2mu\, sin^{2}\theta cos\theta }{2g}\)
\(\frac{mu^{3}\, sin^{2}\theta cos\theta }{2g}\)

Solution

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