A player stops a football weighting 0.5 kg which comes flying towards him with a velocity of 10m/s. If the impact lasts for 1/50th sec. and the ball bounces back with a velocity of 15 m/s, then the average force involved is

250 N
1250 N
500 N
625 N

Solution

Here m = 0.5 kg ; u = –10 m/s ;t = 1/50 s ; v =+ 15 ms^-1 Force = m(v– u)/t = 0.5 (10 + 15) × 50 = 625 N

A toy gun consists of a spring and a rubber dart of mass 16g. When compressed by 4cm and released, it projects the dart to a height of 2 m. If compressed by 6 cm, the height achieved is

3 m
4 m
4.5 m
6 m

Solution

If k is the spring factor,then P.E. of the spring compressed by distance x=\(\left ( \frac{1}{2}kx^{2} \right )\) will equal to gain in P.E. of the dart ( = mgh) i.e.\(\frac{1}{2}kx^{2}\)=mgh
\(\frac{1}{2}k(4)^{2}=16\times g\times 200....(i)\)
and \(\frac{1}{2}k(6)^{2}=16\times g\times h....(ii)\)
On solving, (i) and (ii), we get h = 450 cm = 4.5 m.

A solid sphere of 2 kg is suspended from a horizontal beam by two supporting wires as shown in fig. Tension in each wire is approximately (g = 10 ms^-2)

30 N
20 N
20 N
5 N

Solution

2 T cos 60º = mg
or T = mg = 2×10 = 20N.

An object of mass 10 kg moves at a constant speed of 10 ms^-1. A constant force, that acts for 4 sec on the object,gives it a speed of 2 ms^-1 in opposite direction. The for ceacting on the object is

–3 N
–30 N
3 N
30 N

Solution

Here u= 10 ms^-1, v = –2 ms^-1,t =4 s, a= ?

Using a=\(\frac{v-u}{t}=\frac{-2-10}{4}=-3m / s^{2}\)

∴Force,F = ma = 10×(–3)= –30 N

Directions : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement -1 :The two bodies of masses Mand m (M> m)are allowed to fall from the same height if the air resistance for each be the same then both the bodies will reach the earth simultaneously.

Statement -2 : For same air resistance, acceleration of both the bodies will be same.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(a)Statement -1 is false, Statement-2 is true

The force acting on the body of mass M are its weight Mg acting vertically downward and air resistance Facting vertically upward.

∴ Acceration of the body , a = g - ^F⁄_M

Now M> m, therefore, the body with larger mass will have great acceleration and it will reach the ground first.

Directions : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement -1 :On a rainy day, it is difficult to drive a car or bus at high speed.

Statement -2 :The value of coefficient of friction is lowered due to wetting of the surface.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1

On a rainy day, the roads are wet. Wetting of roads lowers the coefficient of friction between the types and the road. Therefore, grip on a road of car reduces and thus chances of skidding increases.

Directions : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement -1 :The work done in bringing a body down from the top to the base along a friction less incline plane is the same as the work done in bringing it down the vartical side.

Statement -2 :The gravitational force on the body along the inclined plane is the same as that along the vertical side.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(d)Statement -1 is true, Statement-2 is false

Work done in moving an object against gravitational force depends only on the initial and final position of the object, not upon the path taken. But gravitational force on the body along the inclined plane is not same as that along the vertical and it varies with angle of inclination.

A motor cycle is going on an over bridge of radius R. The driver maintains a constant speed. As the motor cycle is ascending on the over bridge, the normal force on it

increases
decreases
remains the same
fluctuates erratically

Solution

R= mg cos θ - ^mV²⁄_r

When θ decreases, cosθ increases i.e. R increases

A spring of force constant k is cut into two pieces whose lengths are in the ratio 1 : 2. What is the force constant of the longer piece ?

^k⁄₂
^3k⁄₂
2 k
3k

Solution

A bullet of mass m is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by adistance d. Then the velocity of the bullet is

\(kd\sqrt{M/m}\)
\(\frac{d}{M}\sqrt{km}\)
\(\frac{d}{m}\sqrt{km-M}\)
\(\frac{kM}{m}\sqrt{d}\)

Solution

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