Explanation

A heat detector is used for finding fires by detecting significant increases in temperature

Types:

Some heat detectors respond to a rapid temperature increase ("rate-of-rise"),

While others activate when a specific temperature is reached ("fixed temperature"). 

Explanation

Explanation

Swimming is a full-body workout that engages multiple muscle groups.

It leading to high energy expenditure.

It is often considered more energy-intensive than jogging, riding, or running due to the resistance of water.

Explanation

Explanation

Explanation

To find the divergence, calculate:

div(f) = ∂/∂x (3x^2) + ∂/∂y (5xy) + ∂/∂z (xyz^3)

= 6x + 5x + 3xyz^2

At (1, 2, 3):

div(f) = 6(1) + 5(1) + 3(1)(2)(3)^2

= 6 + 5 + 54

= 65

Explanation

Bohr's quantum condition states that the angular momentum of an electron in a circular orbit is quantized:

mvr = nh / 2π

where m is the mass of the electron,

v is the velocity,

r is the radius of the orbit,

n is the principal quantum number,

and h is Planck's constant.

Explanation

The acceleration of a particle moving in a uniform circular motion is directed towards the center of the circle and is given by:

a = v^2 / r

This is known as centripetal acceleration.

Explanation

When a spherical ball rolls without slipping:

Total energy (E) = Kinetic energy (K) + Rotational energy (U)

K = (1/2)mv^2

U = (1/2)Iω^2 = (1/5)mv^2 (for a sphere)

E = K + U = (1/2)mv^2 + (1/5)mv^2 = (7/10)mv^2

Fraction of energy associated with rotation:

U/E = ((1/5)mv^2) / ((7/10)mv^2) = 2/7

Explanation

According to the law of universal gravitation:

F ∝ (m1 × m2) / r^2

Initially, F0 ∝ (m × m) / r^2

After doubling the mass and halving the distance:

F_new ∝ (2m × 2m) / (r/2)^2

= 16 × F0