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

The equation of a plane progressive wave is y = 0.9 sin 4 π[t – ^x⁄₂]. When it is reflected at a rigid support, its amplitude becomes ³⁄₂ of its previous value.The equation of the reflected wave is

y = 0.6 sin 4 π[t + ^x⁄₂]
y = -0.6 sin 4 π[t + ^x⁄₂]
y = -0.9 sin 8 π[t - ^x⁄₂]
y = -0.6 sin 4 π[t + ^x⁄₂]

Solution

Amplitude of reflected wave =²⁄₃ × 0.9 = 0.6

It would travel along negative direction of x-axis, and on reflection at a rigid support, there occurs a phase change of π.

For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is

3: π
π: 3
1: π
π: 1

Solution

Two rods of the same length and areas of cross-section A1and A2have their ends at the same temperature. K₁ and K₂ are the thremal conductivities of the two rods. The rate of flow of heat is same in both rods if

\(\frac{A_{1}}{A_{2}}=\frac{K_{1}}{K_{2}}\)
\(\frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}}\)
A₁A₂= K₁K₂
\(A_{1}K_{1}^{2}=A_{2}K_{2}^{2}\)

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

Statement 1 :A positive acceleration can be associated with a ‘slowing down’ of the body.

Statement 2 :The origin and the positive direction of an axis area matter of choice.

(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

A projectile is moving at 60 m/s at its highest point, where it breaks into two equal parts due to an internal explosion.One part moves vertically up at 50 m/s with respect to the ground. The other part will move at a speed of

110 m/s
120 m/s
130 m/s
10\(\sqrt{61}\) m/ s

Solution

A bar magnet 8 cms long is placed in the magnetic merdian with the N-pole pointing towards geographical north. Two netural points separated bya distance of 6 cms are obtained on the equatorial axis of the magnet. If horizontal component of earth’s field = 3.2 × 10^–5T, then pole strength of magnet is

5 ab-amp × c
10 ab-amp × cm
2.5 ab-amp × cm
20 ab-amp × cm

Solution

A current of I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius r. The magnetic field at any point inside the cylinder at a distance x from the axis of the cylinder is

∞
\(\frac{\mu _{0}I}{2\pi r}\)
\(\frac{\mu _{0}I}{2\pi x}\)
zero

Solution

Since no current is enclosed inside the hollow conductor. Hence B_inside= 0.

Angular momentum of a system of a particles changes, when

force acts on a body
torque acts on a body
direction of velocity changes
None of these

Solution

If we apply a torque on a body, then angular momentum of the body changes according to the relation
\(\dot{\tau }=\frac{d\dot{L}}{dt}\Rightarrow if\: \dot{\tau }=0 \: then,\vec{L}=constant\)

If a toroid uses bismuth for its core, the field in the core compared to that in empty core will be slightly

greater
smaller
equal
None of these

Solution

Field in the core with Bismuth will be smaller because bismuth is diamagnetic.

Taking Rydberg’s constant R_H= 1.097 × 10⁷m, first and second wavelength of Balmer series in hydrogen spectrum is

2000 Å, 3000 Å
1575 Å, 2960 Å
6529 Å, 4280 Å
6552 Å, 4863 Å

Solution

A lens of power + 2 diopter is placed in contact with a lens of power –1 diopter. The combination will be have like

a convergent lens of focal length 50 cm
a divergent lens of focal length 100 cm
a convergent lens of focal length 100 cm
a convergent lens of focal length 200 cm

Solution

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

Statement 1 :Energy cannot be divided by volume.

Statement 2 :Because dimensions for energy and volume are different

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

Solution

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

The resistance R of a wire is given by the relation R =\(\frac{\rho \iota }{r^{2}}\).Percentage error in the measurement of r, land r is 1%, 2%and 3% respectively. Then the percentage error in theme asurement of R is :

Solution

A given resistor has the following colour scheme of the various strips on it : Brown, black, green and silver. Its value in ohm is

1.0 × 10⁴ ± 10%
1.0 × 10⁵ ± 10%
1.0 × 10⁶ ± 10%
1.0 × 10⁷ ± 10%

Solution

Numbers attached for brown,black, green and silver are 1, 0, 5, ± 10%. Therefore the resistance of given resistor

= 10 × 10⁵ Ω ± 10% = 10 × 10⁶ Ω ± 10%.

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